What is the equation of the parabola with focus (1,1/2) and directrix y=3

Answers:
A. Y=-1/5x^2+2/5x+31/20
B. Y=-3/16x^2
C. Y=-3/5x^2-14/31x+71/16
D. Y=-x^2+17x-1

Answer:

A. 6i

Step-by-step explanation:

Apply by the radicial rule.

[tex]\sqrt{-36}=\sqrt{-1}\sqrt{36}[/tex]

[tex]\sqrt{-1}\sqrt{36}[/tex]

Imaginary number.

[tex]\sqrt{36 i}[/tex]

Square root the numbers from left to right.

[tex]6^2=36[/tex]

[tex]\sqrt{6^2}=6[/tex]

6i is the correct answer.

I hope this helps you, and have a wonderful day.

Answer:

A

Step-by-step explanation:

Answer:

So a point is (-3,-5) and the vertex is (-4,-3)

Step-by-step explanation:

This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.

The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)

I will choice -3.  This gives -2(-3+4)^2-3

f(-3)=-2(1)^2-3

f(-3)=-2-3

f(-3)=-5

So a point is (-3,-5) and the vertex is (-4,-3)

Answer:(-4,-3)

Step-by-step explanation:

Answer:

  {4}

Step-by-step explanation:

It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.

  f(4) = 13 = g(4)

_____

The functions also have the same value for x=-2, but that is not in the domain given.

Answer:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer B

Step-by-step explanation:

* Lets explain the triangle inequality theorem

- The triangle Inequality Theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side.

- That means when we add the lengths of the shortest two sides,

  the answer will be greater than the length of the longest side.

- Examples:

# Is the set of {4 , 5 , 9} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 9} couldn't form a triangle

# Is the set of {4 , 5 , 8} could form a triangle

- Add 4 , and 5 because they are the shortest sides

∵ 4 + 5 = 9

∵ The third side is 8

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {4 , 5 , 8} could form a triangle

# Is the set of {3 , 5 , 9} could form a triangle

- Add 3 , and 5 because they are the shortest sides

∵ 3 + 5 = 8

∵ The third side is 9

∵ In any triangle the sum of the lengths of any two sides of a triangle

  must be greater than the length of the third side

∴ The set {3 , 5 , 9} couldn't form a triangle

* Lets solve the problem

∵ The triangle inequality theorem is the sum of the lengths of any two

  sides of a triangle is greater than the length of the third side

- It talks about the relation between the lengths of the sides

∴ The right answer is B. The sum of the lengths of any two sides of

   a triangle is greater than the length of the third side

Answer:

B

Step-by-step explanation:

A cannot be correct as it is measuring angles, and the theorem is not abt the angles.

B is correct because the theorem is abt triangle sides.

C is incorrect because that is just ridiculous.

D is incorrect because is not always true and the theorem once again, is not abt angles.

Answer:

  a)  y = x+1

  b)  The transformation shifts the graph 1 unit to the left

Step-by-step explanation:

a) Put (x+1) where (x) is in the function definition:

  y = f(x+1)

  y = x+1

__

b) This transformation has the effect of shifting the graph one unit to the left. Any point (x, f(x)) on the original curve, will now be (x-1, f(x)), shifted one unit to the left.

Answer:

Step-by-step explanation:

No solution

Answer:

First, before I answer, he or she forgot the n/3.

So the problem is n/3 + (-4) = 2

The answer is 6

Step-by-step explanation:

First, simply + -4 to -4, because different signs subtract

Second subtract -4 + 2 which equals 2

Now multiply 3 ( came from n/3) with 2

And its 6

I hope I helped you!!!

No, because AB is 2/5 the length MN but CD is 1/3 the length QP.  

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Given:

As, Comparing the corresponding sides, the length of AB is 4.  

The length of MN is 10.  This makes their ratio 4/10 = 2/5.

and, the CD length is 2.

QP has a length of 6. Consequently, their ratio is 2/6 = 1/3.

Therefore, because the side ratios differ, the figure is not proportionate and is not a dilation.

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Trapezoid ABCD is not the result of the dilation of trapezoid MNPQ by a scale factor of 2/5 because AB is 2/5 the length MN but CD is 1/3 the length QP.

Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.

Given a trapezoid ABCD and another trapezoid MNPQ.

From the figure,

length of AB = 2 + 2 = 4

Length of MN = 5 + 5 = 10

Scale factor = 4/10 = 2/5

Now,

Length of CD = 1 + 1 = 2

Length of QP = 3 + 3 = 6

Scale factor = 2/6 = 1/3

That is, the scale factor differs.

Hence the correct option is C.

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[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-4}{2(1)}~~,~~6-\cfrac{(-4)^2}{4(1)} \right)\implies (2~~,~~6-4)\implies (2~,~2)[/tex]

Answer:

B. (2,2).

Step-by-step explanation:

Convert to vertex form y = a(x - b)^2 + c where (b, c) is the vertex.

y =x^2 - 4x + 6

y = (x - 2)^2 - 4 +6

y = (x - 2)^2 + 2.

Therefore the vertex is (2, 2).

Answer:

  (x, y, z) = (1, -1, -4)

Step-by-step explanation:

A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.

_____

In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.

If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.

In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.

As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.

Answer: A

Step-by-step explanation: edge 2021

ANSWER

[tex]x = 140 \degree[/tex]

EXPLANATION.

The two tangents each meet the radius at 90° each.

This implies that,

[tex]x + 40 + 90 + 90 = 360[/tex]

The sum of interior angles of a Quadrilateral is 360°

We simplify to get

[tex]x + 40 = 180[/tex]

[tex]x = 180 - 40[/tex]

[tex]x = 140 \degree[/tex]

It is best to graph the function when searching for the range.

For the function f(x) = (x + 5)(x + 1), the range is ALL REAL NUMBERS when y is greater than or equal to -4.

Get it?

Answer:

45.71 - 6x

Step-by-step explanation:

If Heather bought markers to donate, the amount she donates is subtracted from her balance of 45.71.  We know she bought 6 packs of markers, but we do not know how much each pack cost.  We will make this our unknown "x".  The expression for  packs of markers costing "x" is 6x.  Because she buys them from her account, which takes aways from her balance, the expression that represents this donation is:

45.71 - 6x

(Notice that the question asks for the EXPRESSION after she buys the markers, not the EQUATION.  The difference between an expression and an equation is the lack of an equals sign in the expression.)

Answer:

M= 45.71 - 6x

Step-by-step explanation:

M represents money and x is how much each pack of markers cost. 45.71, which is the original amount, minus 6x will give the correct amount.

Step-by-step explanation:

This equation is written in standard form, y = ax² + bx + c.

a = 1 , b = -2 , c = -4

First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).

Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-(-2)}{2(1)}[/tex]   Simplify

[tex]\frac{2}{2}[/tex]   Simplify

1

So, the middle of your parabola will be at x = 1.

Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.

y = x² - 2x - 4   Plug in 0

0 = x² - 2x - 4   Factoring won't work, so use the Quadratic Formula.

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]   Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.

[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex]   Simplify

x = 3.235 and -1.235

These are your x-intercepts, where your parabola crosses the x-axis.

Now, just put all of this information together on a graph!

Answer:

Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer

Step-by-step explanation:

* Lets study the meaning independent and dependent probability

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question

∵ P(A) =  watching a movie

∵ P(B) =  going out to dinner

∵ The probability that a person will watch a movie is 62%

∴ P(A) = 62% = 62/100 = 0.62

∵ The probability of going out to dinner is 46%

∴ P(B) = 46% = 46/100 = 0.46

∵ The probability of watching a movie and going out to dinner

  is 28.52%

∵ P(A and B) = 28.52% = 28.52/100 = 0.2852

- Lets find the product of P(A) and P(B)

∵ P(A) = 0.62

∵ P(B) = 0.46

∵ P(A and B) = 0.2852

∴ P(A) · P(B) = 0.62 × 0.46 = 0.2852

∴ P (A and B) = P(A) · P(B)

∴ Watching a movie and going out to dinner are independent events

  because the P(A) · P(B) = P(A and B)

Answer:

c = 25, d = 65

Step-by-step explanation:

∠d + 90 = 155 ( vertical angles )

Subtract 90 from both sides

d = 65

The angle above 155 = 180 - 155 ( straight angle ) = 25

Hence c = 25 ( corresponding angles )

Answer:

<d = 65 degrees.

<c = 25 degrees.

Step-by-step explanation:

<d + 90 = 155 since vertically opposite <'s are equal. Therefore <d = 155-90

= 65 degrees.

The angle adjacent to <d is 180-155= 25 degrees since <'s on a line = 180 degrees.

Therefore <c= 25 degrees since corresponding <'s on parallel lines are equal.

Answer:

[tex](p - 19) \geqslant 47[/tex]

[tex]p \geqslant 66[/tex]

Answer: The required interval notation of the solution is [66, ∞).

Step-by-step explanation:  We are given to translate and solve the following inequality :

"Nineteen less than p is no less than 47".

Also, to write the solution in interval notation.

According to the given information, the inequality can be written as follows :

[tex]p-19\geq47.[/tex]

The solution of the above inequality is as follows :

[tex]p-19\geq47\\\\\Rightarrow p\geq47+19\\\\\Rightarrow p\geq 66.[/tex]

Thus, the required interval notation of the solution is [66, ∞).

Answer:

sqrt of 2/2

Step-by-step explanation:

Answer:

The exact value of cos 45° is: [tex]\frac{\sqrt{2} }{2}[/tex].

Step-by-step explanation:

Answer: A C and E

Step-by-step explanation:

-4+6 (x-2x)^2 36x^2yz-3

(A) (C) (E)

There's a screenshot of the answers below

The answer is:

The correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

To calculate the slugging average or slugging percentage, we need to divide the number of total bases by the total times at bat.

[tex]SluggingAverage=\frac{TotalBases}{TimesAtBat}[/tex]

We know that:

A single means 1 base.

A double means 2 bases.

A triple means 3 bases.

A homerun means 4 bases.

So, we know that:

[tex]Singles=25=25bases\\Doubles=2*10=20bases\\Triples=3*3=9bases\\Homeruns=10*40=40bases\\TimesAtBat=140[/tex]

Then, substituting and calculating we have:

[tex]SluggingAverage=\frac{25bases+20bases+9bases+40bases}{140}[/tex]

[tex]SluggingAverage=\frac{94bases}{140times}=0.671[/tex]

Hence, the correct answer is c.

[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]

Have a nice day!

Hi!

To solve this, first let's decide what quadrant the 135 degrees lies in. Starting in quadrant one, it would end up landing in quadrant 2.

Coordinates:

(cos, sin)

In quadrant 2, the y value (sin) as a coordinate would be positive, therefore our final answer should be positive.

180 - 135 = 45

Therefore our reference angle will be sin45.

We should know that sin45 is equal to [tex]\cfrac{\sqrt{2} }{2}[/tex]

Now, remember that our final answer should be positive. We don't have to change this because it's already positive, so your final answer is:

[tex]\cfrac{\sqrt{2} }{2}[/tex]

The exact value of sin 135 degrees is - (√2)/2.

The unit circle and trigonometric identities can be used to calculate the sine of 135 degrees.

We can determine the location of the point on the unit circle that corresponds to an angle of 135 degrees by utilizing the unit circle. It is located in the third quadrant.

In the first and second quadrants, the sine function is positive; however, the third and fourth quadrants are where it is negative.

We can use the fact that the sine of an angle equals the y-coordinate of the point on the unit circle corresponding to that angle to determine the precise value.

The sine of 135 degrees is negative because the third quadrant's y-coordinate is negative.

We can determine the precise sine value of 135 degrees by using a reference angle.

In the third quadrant, the reference angle for 135 degrees is 45 degrees (180 degrees - 135 degrees).

The sine of a 45-degree angle is (2)/2 or 1/sqrt(2).

The sine of 135 degrees is a negative number because the reference angle is in the third quadrant.

Consequently, (2)/2 is the precise value of sin 135 degrees.

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Answer:

  y = 3

Step-by-step explanation:

The solution is the point where the lines intersect, (x, y) = (6, 3). The y-coordinate of that point is 3.

Answer:

y = 3

Step-by-step explanation:

You must count the lines from the intersection to the Ox axis down.

Answer:

The true statements are:

The y-variable will be eliminated when adding the system of equations

There is only one solution to the system of equations is

Step-by-step explanation:

* Lets explain how to solve the problem

- We use the elimination method to solve the system of the

  linear equation

- The solution is one of three cases

# Exactly one solution ⇒ the 2 lines which represented the equations

  intersect each other at one point

# No solution ⇒ the 2 lines which represented the equations are

  parallel to each other

# Infinite solutions ⇒ the two lines are coincide

- In the system of the linear equations of the problem we have two

 linear equations  -x + 6y = 16 and 8x - 6y = -2

- To solve we must to eliminate one of the two variables

∵ The y's in the two equations have the same coefficients and

   different signs

∴ We add the equations to eliminate y

∴ (-x + 8x) + (6y - 6y) = 16 + -2

∴ 7x = 14 ⇒ divide both sides by 7

∴ x = 2

- Substitute the x in any one of the two equations by 2

∴ -2 + 6y = 16 ⇒ add 2 to both sides

∴ 6y = 18 ⇒ divide both sides by 6

∴ y = 3

∴ The solution of the system of the equations is (2 , 3) ⇒ only one

   solution

- Lets check the statements to find the true statements

# The x-variable will be eliminated when adding the system of

   equations is not true

# The y-variable will be eliminated when adding the system of

   equations is true

# The sum of the system of equations is - x + 6y is not true

# There is only one solution to the system of equations is true

Statements 1 and 2 are true, while statements 3 and 4 are false.

Let's analyze each statement:

1. The x-variable will be eliminated when adding the system of equations.

  - When adding the equations, the x-variables are eliminated because (x) in one equation cancels with (-8x) in the other equation. So, this statement is true.

2. The y-variable will be eliminated when adding the system of equations.

  - When adding the equations, the y-variables are also eliminated because (6y) in one equation cancels with (-6y) in the other equation. So, this statement is true.

3. The sum of the system of equations is -x + 6y.

  - The sum of the two equations is indeed (-x + 6y). Adding the equations directly gives ( -x + 6y = 14), not ( 16). So, this statement is false.

4. There is only one solution to the system of equations.

  - Since the system of equations represents two equations with two variables, the solution can either be a unique solution, no solution, or infinitely many solutions. To determine this, we need to solve the system of equations. We can do this by eliminating one variable and solving for the other. However, from the given equations, we can't determine the nature of the solution without further analysis. So, this statement is indeterminate based solely on the provided equations.

Therefore, statements 1 and 2 are true, while statements 3 and 4 are indeterminate based on the given information.

The equation of Bunny hill ski resort is z = 10x + 35 while z = 5x + 40  for the Black diamond ski resort at the point and at point (1,45) the cost of both will be the same.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say x number of hours a men sky

Then,

Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour

So,

Total cost

z = 35 + 10x

Now,

Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski

So,

Total cost

z = 40 + 5x

Now point where the cost of both resorts will same is

35 + 10x = 40 + 5x

x = 1

So,

z = 40 + 5(1) = 45

Hence, at point (1,45) the cost of both will be the same.

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Final answer:

To find when the costs are the same for both ski resorts, set up an equation based on their rates and solve for the number of hours, which in this case is 1 hour.

Explanation:

To determine at what point the cost of both Bunny Hill Ski Resort and Black Diamond Ski Resort is the same, we can set up an equation based on the given rates.

Let x be the number of hours spent skiing. Then the total cost at Bunny Hill Ski Resort is $35 (ski rental) plus $10 per hour (hourly rate), which is expressed as 35 + 10x.

Similarly, the cost at Black Diamond Ski Resort is $40 (ski rental) plus $5 per hour (hourly rate), or 40 + 5x. To find when the costs are equal, we set the two expressions equal to each other:

35 + 10x = 40 + 5x

Now we can solve for x:

35 + 10x = 40 + 5x
10x - 5x = 40 - 35
5x = 5
x = 1

Thus, after 1 hour of skiing, the cost of skiing at both resorts becomes the same.

Answer:

  Wet Suit Willy

Step-by-step explanation:

To find boxes per dive, divide boxes by dives:

  Sam: 33/11 = 3 . . . boxes per dive

  Willy: 81/18 = 4.5 . . . boxes per dive

  Dan: 104/26 = 4 . . . boxes per dive

Wet Suit Willy found the most treasure boxes per dive: 4.5.

Explanation:

When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.

___

If you have studied vectors, you can find the dot product of AC with BC:

  AC = (-5, 3) -(-2, -3) = (-3, 6)

  BC = (6, 1) -(-2, -3) = (8, 4)

The dot product is ...

  (-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0

When the dot product of vectors is zero, they are perpendicular.

Answer:

Step-by-step explanation:

Add all the students: 4+6+2+2+3+4+6+3 = 30

Add all the male students = 14

divide : 14/30=0.466666

multiply by 100

0.466*100=4.66

round

Answer = 5

Answer:

41

Step-by-step explanation:

plug in each number with the corresponding variable so

5*2-(-3)^2+2*4(2-(-3))

the use pemdas and you get 41

I'm only doing these because it's about a pet pig named Hammy.

5.

rate = distance / time

a.

rate: 36 inches per 3 seconds

b

unit rate: 12 inches per second

c

5 seconds × 12 inches per second = 60 inches

d

144 inches / 12 inches per second = 12 seconds

6.

a.

[tex] \frac 4 7 \div \frac 3 5 = \frac 4 7 \times \frac 5 3 = \dfrac{20}{21}[/tex]

b.

[tex]2 \frac 2 5 \div 1 \frac 7 9 = \frac{12}{5} \div \frac{16}{9} = \frac{12}{5} \times \frac{9}{16} = \dfrac{27}{20} [/tex]

c

[tex]3.24 \div 1.5 = 3.24 \div \frac 3 2 = 3.24 \times \frac 2 3 = 6.48/3 = 2.16[/tex]

d

[tex] \frac 8 9 \div 3\frac 1 3 = \frac 8 9 \times \frac{3}{10} = \dfrac{4}{15}[/tex]

Answer:

Step-by-step explanation:

(a) Hammy's rate is 36 inches in 3 sec.

(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec

(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in

(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec

(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.

(6b) Convert 2  2/5 to 12/5 and 1  7/9 to 16/9.  Then invert the second improper fraction and multiply:  12/5 times 9/16 = 108/80, or 27/20.

(6c)  3.24 divided by 1.5 is equivalent to 3.24 times 2/3:  2.16, or 2  4/25

(6d) 8/9 divided by 3  1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.

Answer:

Step-by-step explanation:

1. Each term has an even coefficient, so a factor of 2 can be removed:

  2(3x^2 +7x -15)

The remaining quadratic factor is prime.

__

2. Each of these two terms is a square, so this is the difference of two squares.

__

3. This cubic has one irrational negative real root. It is prime.

__

4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."

__

5. The magnitude of the x-coefficient is double the square root of the (positive) constant, so this is a perfect square trinomial.

Answer:

Step-by-step explanation: You are given the equation of -7x+6y=9 and -2x-5y=16 and you are asked to find what x=? and what y=?

First step is to write down the problem

-2x-5y=16

next add 5y over the equal sign.

-2x=5y+16

Next is too divide by -2

-2x/-2=5y+16/-2

after solving you get

x=-2.5y-8

now you substitute the equation into the other formula to get

-7(-2.5y-8)+6y=9

then solve by doing -7*-2.5y and -7*-8 to get 17.5y and 56 which will give you

17.5y+56+6y=9

Next you subtract 56 to the other side to get 9-56 or -47 now you have

17.5y+6y=-47

next is too add the 17.5y and 6y together to get 23.5y

23.5y=-47

next is too divide by 23.5

23.5y/23.5=-47/23.5

solve to get y=-2, now this is half you the problem

Step two is too substitute what y=-2 into the equation of x=-2.5y-8 to get

x=-2.5(-2)-8

Solve to get

x=5-8

Solve again to get

x=-3

Your answers are x=-3 and y=-2

Answer:

x = -3 and y = -2

Step-by-step explanation:

It is given that,

-7x + 6y = 9

   ----(1)

-2x - 5y = 16    -------(2)

To find the solution of given equations

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112   ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

-14x - 35y = 112   ---(4)

    0   4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16    -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2