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### Course: Algebra (all content)>Unit 5

Lesson 4: Solving systems of equations with substitution

# Solving linear systems by substitution (old)

An old video where Sal introduces the substitution method for systems of linear equations. Created by Sal Khan.

## Want to join the conversation?

• How would u solve this problem:
{Y=-5x+3
{10x+2y=0
• you have to isolate the y before you substitute
• I can't figure out how to use substitution to solve an equation with 2 variables.
For example:
y= -2x + 10
y= x - 1

• Good evening.
One way would be to substitute the y in Your first equation with the entire right-hand side of Your second equation (which, as You can see, is equal to y):

`y = -2x + 10 : now substitute y for x - 1.
x - 1 = -2x + 10 : add 2x + 1 to both sides.
3x = 11 : divide both sides by 3.
x = 11/3

Use that value to solve for y using one of Your two initial equations, for example:

y = x - 1 : substitute x for 11/3.
y = 11/3 - 1
y = 11/3 - 3/3
y = 8/3

And voilà! You're done!
• This isn't a question but this helped a lot soooooo thanks
• Great! Glad it helped. But you should put it in the tips/thanks next time.
• when writing the equation don't the variables go first?
• It could be place at the end or the front of the equation, but it is recommended to put the variable in the front.
• What would one do if the equation came out X+(-10-8X)=8
I got y=-5-4x though in the equation it 2y did i do it right?
• How would I use substitution method here?
3x + 2y = 15
2x + 6y = 11
• Solve one of the equations for x or y, and then substitute that into the other equation.
• how would you solve y+2+4x
Y+Y=Y
• Ok so far we did questions like y=4x-2 and such but i was wondering how do make the linear line if the equation is y=x²+5 and so...
• What if it was like this ?
x= 2y + 9
x = 5y + 20
• This question isn't exactly the ideal question to use substitution but here:

First step: You have the "x" variables isolated in both equations but you only need it to be isolated in one equation. Therefore, you can move the -9 in the first equation to the other side.
x - 9 = 2y
Second step: You'd want to isolate the y in the first equation so you'd divide by 2 on both sides.
(x - 9) / 2 = y
Third step: In order to make the equation only have one variable, you substitute the second equation in for "x".
((5y + 20) - 9) / 2 = y
Fourth step: Simplify!
(5y + 11) / 2 = y
Fifth step: Keep simplifying!
y = (5/2)y + 11/2
Sixth step: Subtract (5/2)y from both sides to isolate "y".
(-3/2)y = 11/2
Seventh step: Divide both sides by (-3/2).
y = -22/6 = -11/3.
Eighth step: Plug -11/3 in as "y" for the first equation.
x = 2(-11/3) + 9
Ninth step: Simplify!
x = -22/3 + 9
Tenth step: You need common denominators to add fractions so change "9" to "27/3".
x = -22/3 + 27/3