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## 8th grade (Illustrative Mathematics)

### Course: 8th grade (Illustrative Mathematics)>Unit 4

Lesson 11: Lesson 13: Solving systems of equations

# Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120

Learn to solve the system of equations y = -1/4x + 100 and y = -1/4x + 120 using substitution.  Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

Y=3x+7 and...........Y=3x+7
• X can be any real number and y will be whatever that real number is times three and plus seven.
• Wht about a problem like this
-5x+y=-3
3x-8y=24
• Let -5x+y=-3 be the first equation, and 3x-8y=24 be the second. Let's manipulate the first equation by adding 5x to both side; resulting in y=-3+5x, or 5x-3. Now let's plug in 5x-3 for wherever y has been in the second formula. 3x-8(5x-3)=24. This is now pretty straightforward to solve for x. We distribute the 8 into (5x-3) and get 3x-40x-24=24. -48=27x. x=-48/27, x=-16/9.

Now let's plug in the x for either one of the equations to get y. 3(-16/9)+8y=24. -16/3+8y=24. 8y=24+16/3. 24y=72+16. 24y=88. y=88/24, y=11/3.

Hope it helped!
• How do you know what you're supposed to multiply the equations by?
• give an example and i will probably be able to help
• solve for y in terms of x
5x +380y= -2280
• Regina,
Solve for y in terms of x just means "isolate y on one side of the equation".

You do the same thing to both sides of the equation to keep it equal while eliminating everything but the y on the left.

If you first subtract 5x from both sides, the left will have 5x-5x which becomes 0 and disappears leaving you with only 380y on the left.

If you then multiply each side by the reciprocal of 380 (which is 1/380, the 380/380 on the left becomes 1 and disappears leaving you with only y on the left.

Make sure as you do this, you do the same thing to the right side.

When the y becomes isolated on the left, you will have solved for y in terms of x.

I hope that helps make it click for you.
• How do you solve with x/3-y/2=1 and y=2x-2
• Gabby,
x/3-y/2=1
y=2x-2
From the second equation you know that y and 2x-2 are the same so you can substitute (2x-2) for the y in the first equation
x/3-y/2=1 Substiture (2x-2) for the y
x/3 - (2x-2)/2 = 1
Now distribute the -1/2
x/3 - 2x/2 + 2/2 = 1 The 2/2s both become 1
x/3 - 1x +1 = 1 Subtract 1 from both sides
x/3 - 1x = 0
Now, you might just see that x=0 is the solution for x,
Or to combine the x terms, you must find a common denominator.
x/3 - (3/3)x = 0 now 1/3 - 3/3 = -2/3 so
(-2/3)x = 0 Now multiply both sides by the reciprocal of -2/3 which is -3/2
x=0

Now find y by substituting 0 for x in either equation.
y= 2(0) -2
y= 0-2
y= -2

Now double check by substituting 0 for x and -2 for y in the other equation
0/3 - (-2/2) = 1
0-(-1) = 1
1=1
This is true so the answers double check.
x=0 y=-2 or (0,-2)

I hope that helps make it click for you.
• I am still a little bit confused about why the substitution method actually works. Can someone please explain it to me more?
• So, what if the X was solved already for us and the Y would be the thing we would have to solve. Would this apply the same way it does for solving X? Solving Y?
• Yes, solving Y is the same thing as solving X. Lets say that you have x already solved lets say x=3. Now you have to solve for Y. It is the exact same thing. Lets plug what we know into an equation. Lets say that 3+4y=15. Do the same thing you would to find X. If you do your same steps, you will get that Y=4 even doing the same thing you use for X.
(1 vote)
• What is x-y=12
• You can't figure this out with the provided information. It could have multiple answers, which include: (12,0), (100, 88), and infinitely many others.
• How do you solve this problem 4x+3y=2 and 2x+y=6?
(1 vote)
• Line them up like this:
4x+3y=2
2x+y=6
Now ask yourself can i easily solve for x or y, or can I somehow get rid of an x or y?
I see an easy way to solve for y in the second equation:

2x+y=6 therefore y= -2x+6

now we have a function for y in terms of x we can then place it in the top equation and solve for x

4x+3(-2x+6)=2 => 4x-6x+18=2 => -2x=-16 therefore x=8

we can then take this value for x and solve for y using any of the two equations but the second one is more convenient

y= -2x+6 = -2(8)+6=-16+6= -10 therefore y= -10

we can check these results

2(8)-10=6 => 16-6=10 => 10=10 check
4(8)+3(-10)=2 => 32-30=2 => 2=2 check