Does anyone know how to solve by substitution for 1/2x+7=y and 3y-11=-x

Answers

Answer 1
Substitution isn't too difficult to grasp. What you must first come to understand is that in both equations (in this particular problem) x and y are assumed to be the same numbers respectively. Meaning if you looked at the x value of the function: (Keep in mind [tex] \frac{x}{2} [/tex] is the same as [tex] \frac{1}{2} x[/tex])
[tex] y= \frac{x}{2} + 7 [/tex]

It would be the same as the x value in the function: 
[tex]-x = 3y - 11[/tex]

Due to having too many variables we can't solve for a specific variable with the equations in there current form, but because they have equal values of x and y we can solve for x or y and SUBSTITUTE that value for x or y into the other equation! By doing so we eliminate a variable and make it possible to solve that equation for one of the two variables. Luckily they already solved the equations for y in the first one (Keep in mind x, and -x are not the same, thus if you want to use the -x equation you'll need to multiply all numbers by -1.

Explanation aside, let's get to the problem!
 [tex] y= \frac{x}{2} + 7 [/tex]

Now we take that value for y, and substitute it in the other equation wherever there is a y.

[tex]-x = 3[tex]( \frac{x}{2}+7)[/tex]- 11[/tex]

Distribute the 3 to all terms in the parenthesis. (Remember only multiply the numerator by 3! (don't multiply the denominator by 3 is what I'm trying to say)... also if you have forgotten.. the numerator is the top of the fraction and the denominator is the bottom!)

[tex]-x= \frac{3x}{2}+21 - 11 [/tex]

Subtract 11 from 21. 

[tex]-x= \frac{3x}{2}+10[/tex]

Subtract 10 on both sides. 

[tex]-10-x= \frac{3x}{2}+10-10[/tex]

Simplify the right side (10-10 = 0) and add x on both sides!!

[tex]-10 = \frac{3x}{2} +x[/tex]

Add the x's together. To do this gain a common denominator by multiplying the +x by 2/2. Then add it together!

[tex]-10 = \frac{5x}{2} [/tex]

To get x alone we need to remove the fraction. To do that multiply by the fractions reciprocal (flip the fraction and multiply both sides by it. Keep in mind you do not want to multiply by x in this case[tex] \frac{2}{5}*-10 = \frac{5x}{2} * \frac{2}{5} [/tex])

Cancel out the fraction on the right side, and multiply the -10 by 2/5. [tex] \frac{-20}{5} = x[/tex]
x = -4

You probably are thinking... wow that's a lot of work! Well you are somewhat right, but luckily the next part is pretty easy. Pick one of the equations, and plug in the value you got for x and solve for the other variable (y). I'm going to choose the one with y already solved for. 

[tex] \frac{-4}{2} + 7 = y [/tex]
[tex]y = -2 + 7 [/tex]
[tex]y = 5[/tex]

So our answers are: 
x = -4
y = 5



Related Questions

jayson is installing nee flooring in his home if the lenght of the room is 26 feet and the width is 6 feet how many sq feet of flooring does Jayson need

Answers

The equation for area is length * width = area. 
With that said put your numbers into the equation. 
You get: 
26*6=?
Then you will have your answer. 
If you do not know how to do 26*6 do this:
6*6=x
20*6=y
y+x=g
g will be your answer. 
Hope this helps :)

What algebraic expression is 6 more than number c

Answers

The algebraic expression for ''6 more than number c'' is written as;

⇒ c + 6

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''6 more than number c''

Now,

The term ''6 more'' means to ''increase 6'' or to ''add 6''.

Thus, The expression ''6 more than number c'' is written as;

⇒ c + 6

Therefore, The algebraic expression for ''6 more than number c'' is written as;

⇒ c + 6

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What is 5.62 in expanded form

Answers

5.62 = (5 x 1) + (6/10) + (2/100)

Answer:

5.62 = (5 x 1) + (6/10) + (2/100)

Step-by-step explanation:

5.62 = (5 x 1) + (6/10) + (2/100)

Kathleen studied 2/3 of the night's in the month. If the month has 30 days, how many nights did she study?

Answers

This is a proportion problem.
2/3= x/30
Cross multiply and divide
30 x2= 60
60 divided by 3 is 20
Answer is 20


Ps: you could also find the answer by dividing 30 by 3 and that's how you get 1/3 of 3 which is 10. So 2/3 is just 10 + 10= 20

The number of nights studies in a month is 20.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of nights in a month = 30

The number of nights studied in a month.

= 2/3 x 20

= 2 x 10

= 20

Thus,

The number of nights is 20.

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Antonio gave 27 tomatoes to his neighbor and 15 to his brother.he had 72 tomatoes before giving some away.how many tomatoes does Antonio have lefted.

Answers

To figure this out just add 27 and 15 together than subtract that number by 72.
72-15=57-27=30



Antonio has 30 tomatoes left.

Select all the expressions that are equivalent to 735 ÷ 100.

A. 7.35 ÷ 1,000
B. 735 × 0.01
C. 73.5 × 0.001
D. 735 × 0.001
E. 73.5 × 0.1

Answers

B And E All of the rest are wrong <- For 20+ Chars.
all you do this the basic math of each one and see which one matches the answer in the problem which is 7.35.

B. and E are your answers

Graph the equation 18x + 15y = 90 in y=mx+b Please just explain the equation to me you don't have to graph it. It's y=18x+6 right?

Answers

18x + 15y = 90
Subtract 18x to the other side.
15y = -18x + 90
Divide the equation by 15.
y = (-6/5x) + 6

Search y = (-6/5x) + 6 on Google in order to see a picture of the graph if need be.



24 boxes of crayons wigh 235.2 oz. how many oz is each box of crayons?

Answers

The answer is 9.8 ounces per box of crayons

broccoli cost 1.50 per pound at a grocery store. how much does 64 ounces of broccoli cost, before tax

Answers

$6

16 oz = 1 lb
64/16 = 4
4* 1.5 = 6

6 usd for 64 oz 
1 lb = 16 oz

1.50 / 16 = x / 64.....1.50 to 16 oz = x to 64 oz
cross multiply
(16)(x) = (1.50)(64)
16x = 96
x = 96/16
x = 6....so it costs $ 6 for 64 oz

Coach brown bought 6 basketballs for $16 each and 6 footballs for $24 each. The expression 6× 16+6×24 gives the total cost in dollars of the basketballs and footballs. Use the distributive property to write the expression another way. Then evaluate.

Answers

you could say like 12×30
Then the answer to 12x30 would be 360

Bradley's TV screen is 15 feet by 20 feet he wants to put new covers on the TV screen that cost $25 per square foot how much will it cost to cover his TV screen

Answers

25×15 and 25×20 thats the answer

f(x)=x^2-x-1 , average rate of change of f over interval -1 greater than or equal to x less than or equal to 1

Answers

To start, calculate your endpoints of your interval. Do this by plugging in your limits on x, -1 and 1, into your function. This gives you f(-1)=(-1)^2-(-1)-1=1+1-1=1 and f(1)=1^2-1-1=-1. Now, use your two endpoints, (-1,1) and (1,-1), and use the formula for slope, [tex]m= \frac{y_2-y_1}{x_2-x_1} [/tex]. This gives you [tex]m= \frac{-1-1}{1-(-1)} = \frac{-2}{2} =-1[/tex]. This means your average rate of change is -1.
Final answer:

The average rate of change of the function f(x)=x^2-x-1 over the interval from -1 to 1 is calculated as the change in the function's values over the change in x, which results in -1.

Explanation:

The average rate of change of a function f(x) over a given interval [a, b] is defined as the change in f(x) divided by the change in x. It is equal to the value of the function at point b minus the value of the function at point a, divided by (b-a).

For the function f(x)=x^2-x-1, we are given the interval from -1 to 1. In this case, a=-1 and b=1.

So first calculate f(a) and f(b), i.e., f(-1) = (-1)^2 -(-1)-1 = 1, and f(1) = (1)^2 -(1)-1 = -1.

Then, plug these values into the average rate of change formula, which gives us (-1-1) / (1 - (-1)) = -2 / 2 = -1. So the average rate of change of the function f over the interval from -1 to 1 is -1.

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Curtis school has 1,575 students. The students to teacher ratio is 15 to 1. How many teachers are at Curtis school.

Answers

you can set up a ratio and cross multiply and divide
put 15 divided by 1 as one ratio and set up a second where it has 1575 divided by X
then you can cross multiply and divide, so it's 1575 times 1 then divided by 15 and you should get x, which is 105. so 105 teachers for 1575 students

Feel free to rank brainliest! :))

12% of 72 is what number?

Answers

i hope this helps you ?.12%=72 ?.12=72.100 ?=6.100 ?=600

Answer:

x = 8.64

Step-by-step explanation:

12% of 72 = (12/100) * 72/x

= 0.12 * 72

x = 8.64

8.64 is 12% of 72. Determining any kind of percentage will not be a challenge for anybody if the above procedure is followed step by step.

(I think you are in the same county like me. Is it Dadeschools in Miami. Oh and the the Chapter is Chapter 2 Lesson 3 "The Percent Proportion" right?....)

You must be a 12 Grader by now...

find the sum of 28 and 59 show your work

Answers

1. The answer
28. Is 87
+ 59
-----------
87
59+28=87. because 

59+
28
--------
     9 +8=17 so you keep the 7 and put the 1 on top of the 2=5
2+5= 7 7+1= 8, so your final answer would be 87

Yolanda and her 3 brothers shared a box of 156 toy dinosaurs. About how many Dino's did each child get?

Answers

Final answer:

Yolanda and her 3 brothers are sharing 156 toy dinosaurs. By dividing 156 by the total number of children, which is 4, we find that each child gets 39 toy dinosaurs.

Explanation:

The question requires us to divide a certain number of items, specifically toy dinosaurs, equally among a group of children. Yolanda and her 3 brothers share a total of 156 toy dinosaurs. To find out how many dinosaurs each child gets, we need to perform a simple division operation.

Since there are 4 children in total (Yolanda plus her 3 brothers), we divide the total number of toy dinosaurs by 4:

156 toy dinosaurs ÷ 4 children = 39 toy dinosaurs per child

Therefore, each child would receive approximately 39 toy dinosaurs.

Final answer:

To determine how many toy dinosaurs each child receives, divide 156 (the total number of dinosaurs) by 4 (the number of children), resulting in 39 dinosaurs per child.

Explanation:

The subject of this question is Mathematics, and it belongs to the Middle School grade level. The question involves dividing a set of items equally among a group of children, which is a basic arithmetic problem.

Yolanda and her 3 brothers together make a group of 4 children. To find out how many toy dinosaurs each child gets, we divide the total number of toy dinosaurs by the number of children:

Total number of toy dinosaurs: 156
Number of children: 4

Number of dinosaurs per child = 156 ÷ 4
= 39

So, each child would receive approximately 39 toy dinosaurs.

how fast does a ferrari go?

Answers

Depends what Ferrari car it is.
it travels 211 miles per hour

A square room has a tiled floor with 81 square tiles. How many tiles are along an edge of the room?

Answers

As there are 81 tiles total, that makes your area 81. Being a square, that makes your area equation A=s^2. As you need a side, this makes your equation s=√A. Plugging in 81 as A, we get s=√81=9, so an edge has 9 tiles.

There are 9 tiles are along an edge of the room.

Here,

A square room has a tiled floor with 81 square tiles.

What is Area of a square?

In square all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side.

Now,

A square room has a tiled floor with 81 square tiles.

Number of tiles on edge of the room is equal to length of one side of the room.

Hence, we have to find the length of each side of a square room.

For this,

Area of square room = [tex]side^{2}[/tex] = [tex]81[/tex]

⇒ side = √81 = 9

So, There are 9 tiles are along an edge of the room.

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About 3,500 different species of mosquitoes exist in the world if a mosquito traveled 10.8 miles at top speed in 99 hours, how far did it travel in one hour?

Answers

Final answer:

The mosquito traveled approximately 0.109 miles in one hour.

Explanation:

In order to calculate how far the mosquito traveled in one hour, we can use the formula:

Distance = Speed × Time

Given that the mosquito traveled 10.8 miles in 99 hours, we can plug these values into the formula:

Distance = 10.8 miles × 1 hour = 0.109 miles per hour

So, the mosquito traveled approximately 0.109 miles in one hour.

Final answer:

Mosquito populations in Brazil would likely decrease under hot (above 30°C) and dry (below 60% humidity) conditions due to the limited ability of parous females to produce offspring in such conditions, impacting the spread of mosquito-borne diseases.

Explanation:

The question involves evaluating how environmental conditions can affect mosquito populations. Based on the data given, if the climate in Brazil shifted to very hot (above 30°C) and very dry (below 60% humidity) conditions, the mosquito populations would likely decrease. The upper temperature limit for parous females, which are females that have produced viable offspring, is around 30°C. Warmer temperatures would lead to a decline in offspring production. Similarly, very dry conditions (below 60% humidity) would negatively impact mosquito populations, possibly diminishing them further. This information is crucial for understanding mosquito behavior and the spread of diseases such as the West Nile virus, for which mosquitoes are vectors. Efforts to control mosquito populations through environmental management, genetic modification, and other disease prevention strategies are significant to public health.

Carl wants to fill up his fish tank with water. To determine the amount of water that it will take to fill the tank, Carl needs to calculate the ____________ of the tank. A) area B) volume C) perimeter D) lateral area

Answers

Answer:

The answer is B. Volume

Step-by-step explanation:

Finding the area of the tank would only show the size of one of the panals. The perimater is the length around one of the side panels of the tank. Lateral area is simmiler to the surface area, howerver it excludes the base and top. Volume is the only answer choice that calculates how much water will fill the tank. Volume can be found by multiplying the base multiplyed my the length multiplyed by the hight.

Answer:

b volume

Step-by-step explanation:

What digit in the serial number of this dollar bill occurs most often? 6,8,5,8,2,8,5,8

Answers

8 occurs most often.

Answer:

8

Step-by-step explanation:

sorry if this its old

2000g 75.75kg 5050g 3kg order then from smallest to gretest

Answers

Try to convert all of them, in one kind of unit, Here we will do for Kgs,
as we know, 1 kg = 1000 g
so, 2000g = 2 kg & 5050g = 5.050 Kg

Now, Arranging from smallest to greatest :
2 Kg < 3 Kg < 5.050 Kg < 75.75 Kg

In the end, you can re-replace the values, it would be:
2000 g < 3 Kg < 5050 g < 75.75 Kg

Hope this helps!

3p-4=8and 2p=4 is it equivalent

Answers

3p-4=8
+4 on both sides to get
3p=12
divide each side by 3 to get p=4

2p=4
divide off 2 on both sides to get
p=2

Is 2=4? If it is then it is equivelent, if it isnt then theyre not.
3p-4=8
3p=12
p=4

2p=4
p=2

So no, they are not equivalent.

Hope this helps :)

$4.30 markup, 40% discount, 6% tax

Answers

4.30 = 100% 
1% = 0.043
40% = 1.72
6% = 0.258

everything = 6.278 $

Tom practiced piano 1 1/3 hours on Monday and 5/6 hours on Tuesday. how much did he practice in all those two days

Answers

i believe the answer is 4.5 hours

19.25 X 0.12=
please show work

Answers

Your answer will be 2.31, cant really show work, on here.
its 2.31 because you multiply 0.12 by 19.25 and toy will get 2.31

What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4)?
A. y−4=−1/5(x+8)
B. y+4=−9/11(x−8)
C. y−4=−9/11(x+8)
D. y+4=−1/5(x−8)

Answers

Answer:

C. [tex]y-4=-\frac{9}{11}(x+8)[/tex]

Step-by-step explanation:

The point slope form is  [tex]y-y_1=m(x-x_1)[/tex] where m is the slope,

First we are going to calculate [tex]m[/tex]:

If you have two points:

[tex]A=(x_1,y_1)\\B=(x_2,y_2)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case: A=(-8,4) and B=(3,-5)

[tex]x_1=-8, y_1=4\\x_2=3, y_2=-5[/tex]

Replacing in the formula:

[tex]m=\frac{-5-4}{3-(-8)}=-\frac{9}{11}[/tex]

Then [tex]y-y_1=-\frac{9}{11}(x-x_1)[/tex],

Now we have to replace with: [tex]x_1=-8, y_1=4[/tex],

[tex]y-y_1=-\frac{9}{11}(x-x_1)\\\\y-4=-\frac{9}{11}(x-(-8))\\\\y-4=-\frac{9}{11}(x+8)[/tex]

Then the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) is:

C. [tex]y-4=-\frac{9}{11}(x+8)[/tex]

what is 34 divided by 594 LONG DIVISION

Answers

It would be 0.05723 if you do 34 divided by 594.
But 594 divided by 34 would equal 17.4705

Answer:

thanks

Step-by-step explanation:

8465+485744-37493

Regina purchased 1.75 pounds of turkey breast from her local deli for $5.99 per pound. To the nearest cent, how much did she spend at all?

Answers

5.99 per pound * 1.75 pounds purchased = $10.4825. If you round it, she spent $10.48

Marley made 80% of what she made last week. If she $72 this week how much did he make last week?

Answers

The answer is 57 make this a brainliest answer
72 / 0.8 = 90

Therefore $90 was made the week before
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