This is pretty challenging not gonna lie

If you practice a lot and have a good teacher, it'll get less challenging.

I am curious if there are times when either the elimination method or the substitution method would be more appropriate, and or if there would be times when only one way or the other would work. Thank you for the advice in advance!

Yes, both equations will always work, but yes, at times it is more logical to use one over the other. for instance: x-4y=6 x+4y=12 we see here that elimination would best fit: x+x+4y-4y=6+12 or: x=2y-3 7x+3y-81=23 substitute (2y-3) for x. Also, once you have a single placeholder, put it ito quadratic form (ax^2+bx+c=0) and use the quadratic formula: x=(-b±sqrt(b^2-4ac))/2a

how do I solve y=2x-1 and y=3x+2 using the substitution method

You would set them equal to each other because they both equal "y": 2x-1=3x+2

This is so hard I can't.

This is the review. Start at the beginning of the lesson. Go thru each video step by step and make sure you understand before moving to the next one. Ask specific questions when there is some part of the video that you don't understand. As you do the practice problems, if you get one wrong, use the hints to learn from your mistakes. Then, come back and try the review again.

In example 2, when it says we have to solve for x or y, how do I get -2x+y=9 into slope intercept form? And also, how did we get rid of the negative once it was in slope intercept form? Thanks

You cannot get rid of negatives if they are there, so let the signs work themselves out. To isolate the y, all you need to do is add 2x on both sides to get y=2x+9.

Main content

8th grade

Course: 8th grade > Unit 4

Lesson 3: Solving systems with substitution

Substitution method review (systems of equations)

Google Classroom

The substitution method is a technique for solving a system of equations. This article reviews the technique with multiple examples and some practice problems for you to try on your own.

What is the substitution method?

The substitution method is a technique for solving systems of linear equations. Let's walk through a couple of examples.

Example 1

We're asked to solve this system of equations:

\begin{aligned} 3 x + y & = - 3 \\ x & = - y + 3 \end{aligned}

The second equation is solved for

x

, so we can substitute the expression

- y + 3

in for

x

in the first equation:

\begin{aligned} 3 x + y & = - 3 \\ 3 (- y + 3) + y & = - 3 \\ - 3 y + 9 + y & = - 3 \\ - 2 y & = - 12 \\ y & = 6 \end{aligned}

Plugging this value back into one of our original equations, say

x = - y + 3

, we solve for the other variable:

\begin{aligned} x & = - y + 3 \\ x & = - (6) + 3 \\ x & = - 3 \end{aligned}

The solution to the system of equations is

x = - 3

y = 6

We can check our work by plugging these numbers back into the original equations. Let's try

3 x + y = - 3

\begin{aligned} 3 x + y & = - 3 \\ 3 (- 3) + 6 & \overset{?}{=} - 3 \\ - 9 + 6 & \overset{?}{=} - 3 \\ - 3 & = - 3 \end{aligned}

Yes, our solution checks out.

Example 2

We're asked to solve this system of equations:

\begin{aligned} 7 x + 10 y & = 36 \\ - 2 x + y & = 9 \end{aligned}

In order to use the substitution method, we'll need to solve for either

x

y

in one of the equations. Let's solve for

y

in the second equation:

\begin{aligned} - 2 x + y & = 9 \\ y & = 2 x + 9 \end{aligned}

Now we can substitute the expression

2 x + 9

in for

y

in the first equation of our system:

\begin{aligned} 7 x + 10 y & = 36 \\ 7 x + 10 (2 x + 9) & = 36 \\ 7 x + 20 x + 90 & = 36 \\ 27 x + 90 & = 36 \\ 3 x + 10 & = 4 \\ 3 x & = - 6 \\ x & = - 2 \end{aligned}

Plugging this value back into one of our original equations, say

y = 2 x + 9

, we solve for the other variable:

\begin{aligned} y & = 2 x + 9 \\ y & = 2 (- 2) + 9 \\ y & = - 4 + 9 \\ y & = 5 \end{aligned}

The solution to the system of equations is

x = - 2

y = 5

Want to learn more about the substitution method? Check out this video.

Practice

Problem 1

Solve the following system of equations.

\begin{aligned} - 5 x + 4 y & = 3 \\ x & = 2 y - 15 \end{aligned}

x =

y =

Want more practice? Check out this exercise.

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Matt
Posted 7 years ago. Direct link to Matt's post “I am curious if there are...”
I am curious if there are times when either the elimination method or the substitution method would be more appropriate, and or if there would be times when only one way or the other would work. Thank you for the advice in advance!
Button navigates to signup pageComment on Matt's post “I am curious if there are...”
(48 votes)
Answer
- Matthew Johnson
  Posted 7 years ago. Direct link to Matthew Johnson's post “Yes, both equations will ...”
  Yes, both equations will always work, but yes, at times it is more logical to use one over the other. for instance:
  x-4y=6
  x+4y=12
  
  we see here that elimination would best fit:
  x+x+4y-4y=6+12
  
  or:
  x=2y-3
  7x+3y-81=23
  
  substitute (2y-3) for x.
  
  Also, once you have a single placeholder, put it ito quadratic form (ax^2+bx+c=0)
  and use the quadratic formula:
  x=(-b±sqrt(b^2-4ac))/2a
  Comment on Matthew Johnson's post “Yes, both equations will ...”
  (34 votes)
David
Posted 4 years ago. Direct link to David's post “This is pretty challengin...”
This is pretty challenging not gonna lie
Button navigates to signup pageComment on David's post “This is pretty challengin...”
(50 votes)
Answer
- Faeth, Laura P2
  Posted 3 years ago. Direct link to Faeth, Laura P2's post “If you practice a lot and...”
  If you practice a lot and have a good teacher, it'll get less challenging.
  Comment on Faeth, Laura P2's post “If you practice a lot and...”
  (15 votes)
Nancy Crisp
Posted 4 years ago. Direct link to Nancy Crisp's post “how do I solve y=2x-1 and...”
how do I solve y=2x-1 and y=3x+2 using the substitution method
Button navigates to signup pageComment on Nancy Crisp's post “how do I solve y=2x-1 and...”
(7 votes)
Answer
- hmd1114
  Posted 3 years ago. Direct link to hmd1114's post “You would set them equal ...”
  You would set them equal to each other because they both equal "y": 2x-1=3x+2
  Button navigates to signup page
  (5 votes)
Theo Lesko
Posted 4 years ago. Direct link to Theo Lesko's post “are there any easy tips o...”
are there any easy tips or tricks i can use to remember this?
Button navigates to signup pageComment on Theo Lesko's post “are there any easy tips o...”
(11 votes)
Answer
kenaniah
Posted 2 years ago. Direct link to kenaniah's post “This is so hard I can't.”
This is so hard I can't.
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “This is the review. Star...”
  This is the review. Start at the beginning of the lesson. Go thru each video step by step and make sure you understand before moving to the next one. Ask specific questions when there is some part of the video that you don't understand.
  
  As you do the practice problems, if you get one wrong, use the hints to learn from your mistakes.
  
  Then, come back and try the review again.
  Button navigates to signup page
  (9 votes)
LeeAnn Morales
Posted 4 months ago. Direct link to LeeAnn Morales 's post “Lol this is actually kind...”
Lol this is actually kind of simple, though it takes a different mindset. I like to think of the first equation as the problem I'm trying to solve and the second as a hint. See the second one says what x equals even if it doesn't necessarily give you the answer. Because it doesn't give the answer for y, we have to replace the x with the second equation to be able to solve for it. After solving for y, you would plug y into one of the two original equations and solve for x the way you did for y. After you solve for x, you would have the two answers you needed, x and y :) (I hope this was helpful, sorry if it wasn't :[ ...)
Button navigates to signup pageComment on LeeAnn Morales 's post “Lol this is actually kind...”
(8 votes)
Answer
joshh
Posted 5 months ago. Direct link to joshh's post “Practice Solutions: Firs...”
Practice Solutions:

First system of equations:

1st equation: -5x + 4y = 3
2nd equation: x = 2y - 15

Substitute for x:
-5(2y - 15) + 4y = 3

Solve for y:
-10y + 75 + 4y = 3
-6y = -72
y = 12

Solve for x by substituting in one of the equations:
x = 2y - 15
x = 2(12) - 15
x = 9

Check your solution by substituting for x and y in the first equation:

-5x + 4y = 3
-5(9) + 4(12) = 3
-45 + 48 = 3
3 = 3 √

Second system of equations:

5x - 7y = 58

y = -x + 2

Subsitute for y:
5x - 7(-x + 2) = 58

Solve for x:
5x + 7x - 14 = 58
12x - 14 = 58
12x = 58 + 14
x = 72/12
x = 6

Solve for y by substituting in one of the equations:
y = -x + 2
y -(6) + 2
y = -4

Check your solution by substituting for x and y in the first equation:

5x - 7y = 58
5(6) - 7(-4) = 58
30 + 28 = 58
58 = 58 √

I hope this could help someone. It seems like a lot, but once you understand the steps and get the hang of it, it will become pretty quick!
Button navigates to signup pageComment on joshh's post “Practice Solutions: Firs...”
(8 votes)
Answer
Emmery
Posted 4 years ago. Direct link to Emmery's post “In example 2, when it say...”
In example 2, when it says we have to solve for x or y, how do I get -2x+y=9 into slope intercept form? And also, how did we get rid of the negative once it was in slope intercept form?
Thanks
Button navigates to signup pageComment on Emmery's post “In example 2, when it say...”
(5 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “You cannot get rid of neg...”
  You cannot get rid of negatives if they are there, so let the signs work themselves out. To isolate the y, all you need to do is add 2x on both sides to get y=2x+9.
  Comment on David Severin's post “You cannot get rid of neg...”
  (6 votes)
ukldranzer
Posted 5 months ago. Direct link to ukldranzer's post “this takes ages!”
this takes ages!
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(7 votes)
Answer
- P3 Gauthier, Anastasia
  Posted a day ago. Direct link to P3 Gauthier, Anastasia's post “ikr it does”
  ikr it does
  Button navigates to signup page
  (1 vote)
Jaiden Galecki
Posted 10 months ago. Direct link to Jaiden Galecki's post “who is up for quiz one”
who is up for quiz one
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(6 votes)
Answer