Are you supposed to use the substitution method whenever you see the systems of equations?

Systems of equations can be solved by graphing, elimination, or substitution. Which one you use comes down to the systems of equations you're solving for, and how much work you want to do. Some systems solve easier using elimination, while others solve quickly using substitution.

What if the problem is -5x + y= -2 -3 + 6y= -12 How would I figure out either the x value first or the y value first ?

You were already given the Y value, look: -5x + y = -2 -3 + 6y = -12 y = -2 + 5x 6y = -9 y = -9/6 y = -3/2 <--- this is your Y value Y = -9/3 (which is the same as -3/2), all you have to do to solve for X is substitute your Y value into the equation: -5x + 7 = -2 Here it goes: -5x - 2/3 = -2 -5x = -2 +(2/3) -5x = -4/3 x = (-4/3

how would you solve this problem x+y+7z=21 x+y+9z=29 x+y+4z=39

If you subtract the first one from the second one, you find that z = 4. If you subtract the third one from the second one, you find that z = -2. So, those equations don't have a solution.

what if you have a problem like this: -3x - 4y = 2 3x + 3y = -3 ?

thanks so much! I needed help on this and now I have it!

Solve by substitution. System A and System B 3x-5y=13 2x+y=4

In the second equation, isolate y on the left by subtracting 2x from both sides. Now plug the new right hand side of equation two (i.e. 4 - 2x) for y in the top equation. The top equation is now in just one variable: x. Solve this for x. Plug this value for x into either equation and solve for y. Please comment with your answer or any problems you run into.

what if you were to have -7x+8y=-5/ -2x+6y=6?

-7x+8y=-5 AND -2x+6y=6 Solving by substitution: Step 1: solve one of the equations for one of the variables. Pick either equation and either variable, just whichever is convenient. -2x+6y=6 Divide both sides by -2 to get: x - 3y = - 3 Add 3y to both sides to get: x = 3y - 3 Use this to substitute for x into the other equation: -7x+8y=-5 -7(3y - 3) + 8y = -5 -21y + 21 + 8y = -5 Add -21 to both sides to get: -21y + 8y = -26 Combine like terms to get: -13y = -26 Divide both sides by -13 to get: y = 2 Plug y= 2 into one of the equations and solve for x: x = 3y - 3 x = 3(2) - 3 x = 3

What happens if there are more than 2 equations for solving systems with substitution?

You need as many equations as you have variables, so if you have three equations and three unknowns, you can use substitution, but it might be harder to substitute.

Main content

8th grade

Course: 8th grade > Unit 4

Lesson 3: Solving systems with substitution

Systems of equations with substitution: y=4x-17.5 & y+2x=6.5

Name: Systems of equations with substitution: y=4x-17.5 & y+2x=6.5
Uploaded: 2011-02-20T16:28:45Z
Description: Learn to solve the system of equations y = 4x - 17.5 and y + 2x = 6.5 using substitution.

CCSS.Math:

8.EE.C.8

8.EE.C.8b

Google Classroom

Learn to solve the system of equations y = 4x - 17.5 and y + 2x = 6.5 using substitution. Created by Sal Khan and Monterey Institute for Technology and Education.

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Dolotinab
Posted 11 years ago. Direct link to Dolotinab's post “Are you supposed to use t...”
Are you supposed to use the substitution method whenever you see the systems of equations?
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(5 votes)
Answer
- Jared
  Posted 10 years ago. Direct link to Jared's post “Systems of equations can ...”
  Systems of equations can be solved by graphing, elimination, or substitution. Which one you use comes down to the systems of equations you're solving for, and how much work you want to do. Some systems solve easier using elimination, while others solve quickly using substitution.
  Button navigates to signup page
  (6 votes)
Brianna J.
Posted 11 years ago. Direct link to Brianna J.'s post “What if the problem is ...”
What if the problem is

-5x + y= -2

-3 + 6y= -12

How would I figure out either the x value first or the y value first ?
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(4 votes)
Answer
- skeit079
  Posted 11 years ago. Direct link to skeit079's post “You were already given th...”
  You were already given the Y value, look:
  
  -5x + y = -2 -3 + 6y = -12
  y = -2 + 5x 6y = -9
  y = -9/6
  y = -3/2 <--- this is your Y value
  
  Y = -9/3 (which is the same as -3/2), all you have to do to solve for X is substitute your Y value into the equation: -5x + 7 = -2
  
  Here it goes:
  
  -5x - 2/3 = -2
  -5x = -2 +(2/3)
  -5x = -4/3
  x = (-4/3
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  (4 votes)
P B
Posted 9 years ago. Direct link to P B's post “how would you solve this ...”
how would you solve this problem
x+y+7z=21
x+y+9z=29
x+y+4z=39
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(4 votes)
Answer
- Sid
  Posted 9 years ago. Direct link to Sid's post “If you subtract the first...”
  If you subtract the first one from the second one, you find that z = 4.
  If you subtract the third one from the second one, you find that z = -2.
  So, those equations don't have a solution.
  Button navigates to signup page
  (2 votes)
Brianna J.
Posted 11 years ago. Direct link to Brianna J.'s post “what if you have a proble...”
what if you have a problem like this:

-3x - 4y = 2

3x + 3y = -3

?
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(2 votes)
Answer
- Brianna J.
  Posted 11 years ago. Direct link to Brianna J.'s post “thanks so much! I needed ...”
  thanks so much! I needed help on this and now I have it!
  Button navigates to signup page
  (3 votes)
justinheard
Posted 10 years ago. Direct link to justinheard's post “Solve by substitution. Sy...”
Solve by substitution.
System A and System B
3x-5y=13
2x+y=4
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(2 votes)
Answer
- newbarker
  Posted 10 years ago. Direct link to newbarker's post “In the second equation, i...”
  In the second equation, isolate y on the left by subtracting 2x from both sides. Now plug the new right hand side of equation two (i.e. 4 - 2x) for y in the top equation. The top equation is now in just one variable: x. Solve this for x. Plug this value for x into either equation and solve for y.
  
  Please comment with your answer or any problems you run into.
  Button navigates to signup page
  (2 votes)
gabrielle barton
Posted 8 years ago. Direct link to gabrielle barton's post “How do you solve by subst...”
How do you solve by substitiution??
3x-2y=7
x+2y=5
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(2 votes)
Answer
jennyfer mendoza
Posted 8 years ago. Direct link to jennyfer mendoza's post “I don't understand how to...”
I don't understand how to make one that looks like this:

-5x+3y=1
4x+y=23
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(1 vote)
Answer
Jessica Torres
Posted 10 years ago. Direct link to Jessica Torres's post “what if you were to have ...”
what if you were to have -7x+8y=-5/ -2x+6y=6?
Button navigates to signup pageComment on Jessica Torres's post “what if you were to have ...”
(1 vote)
Answer
- Just Keith
  Posted 10 years ago. Direct link to Just Keith's post “-7x+8y=-5 AND -2x+6y=6 S...”
  -7x+8y=-5 AND -2x+6y=6 Solving by substitution:
  Step 1: solve one of the equations for one of the variables. Pick either equation and either variable, just whichever is convenient.
  -2x+6y=6
  Divide both sides by -2 to get: x - 3y = - 3
  Add 3y to both sides to get: x = 3y - 3
  Use this to substitute for x into the other equation:
  -7x+8y=-5
  -7(3y - 3) + 8y = -5
  -21y + 21 + 8y = -5
  Add -21 to both sides to get: -21y + 8y = -26
  Combine like terms to get: -13y = -26
  Divide both sides by -13 to get: y = 2
  Plug y= 2 into one of the equations and solve for x:
  x = 3y - 3
  x = 3(2) - 3
  x = 3
  Button navigates to signup page
  (4 votes)
Laeeqa Ahmad
Posted 11 years ago. Direct link to Laeeqa Ahmad's post “The problem is 840=(x+y) ...”
The problem is 840=(x+y) eq.1 & 840=(y-x)7 need to understand how to solve in substitution method HELP?
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(2 votes)
Answer
David White
Posted 2 months ago. Direct link to David White's post “What happens if there are...”
What happens if there are more than 2 equations for solving systems with substitution?
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(1 vote)
Answer
- David Severin
  Posted 2 months ago. Direct link to David Severin's post “You need as many equation...”
  You need as many equations as you have variables, so if you have three equations and three unknowns, you can use substitution, but it might be harder to substitute.
  Button navigates to signup page
  (2 votes)

Video transcript

We have this system of equations, y is equal to 4x minus 17.5, and y plus 2x is equal to 6.5. And we have to solve for x and y. So we're looking for x's and y's that satisfy both of these equations. Now, the easiest way to think about it is we've already solved for y in this top equation. Let me write it again. I'll write it in pink. We have y is equal to 4x minus 17.5. So this first equation is telling us, literally, by this constraint, y should be 4 times x minus 17.5. Now, the second equation says whatever y is, we had 2 times x, and that should be 6.5. Well, the y here also has to meet this constraint up here. It also has to meet the constraint that it has to be 4 times x minus 17.5. So what we can do is, is we can substitute this value for y into this equation. Let me be clear what I'm doing. The second equation here is y plus 2x is equal to 6.5. We know that y has to be equal to this thing right here. y has to be equal to 4x minus 17.5. So let's take 4x minus 17.5, and substitute y with that. So let's put that right there. So if we were to do that, if we were to replace this y with 4x minus 17.5, because that's what the first equation is telling us, then we get 4x minus 17.5, plus 2x is equal to 6.5. And now we have a single linear equation with one unknown. Let's solve for x. So first we have our x terms. We have a 4x, and we have a 2x. We can group them or add them together. 4x plus 2x is 6x. And then we have 6x minus 17.5 is equal to 6.5. Then we can get the 17.5 out of the way by adding it to both sides of the equation. So this is negative 17.5, so let's add positive 17.5 to both sides of this equation. And we are left with the left-hand side is just going to be 6x, because these guys cancel out. 6x is going to be equal to-- and 6.5-- see, 6 plus 17 is 23, and then 0.5 plus 0.5 is 1. So this is going to be 24. And then we can divide both sides of this equation by 6. And you are left with x is equal to 24 over 6, which is the same thing as 4. So we figured out the x value for the x and y pair that satisfy both of these equations. Now we need to figure out the y value. And we can do that by taking this x and putting it back into one of these equations. We can do it in to either one. We should get the same y value. So let's just do this top one up here. So if we assume x is equal to 4, this top equation tells us y is equal to 4 times x, which in this case is 4, minus 17.5. Well, this is equal to 16 minus 17.5, which is equal to negative 1.5. So y is equal to negative 1.5. So the solution to this system is x is equal to 4, y is equal to negative 1.5. And you can even verify that these two, they definitely work for the top one if you put 4 times 4, minus 17.5, you get negative 1.5. But they also work for the second one. And let's do that. In the second one, if you take negative 1.5, plus 2 times x-- plus 2 times 4-- what does that equal? That's negative 1.5 plus 8. Well, negative 1.5 plus 8 is 6.5. So this x and y satisfy both of these equations.