Question

How do you solve the following linear system: `2x+3y=13 , y-3=-2x`?

Answer 1

You factor by substitution!

Explanation:

First, write down your two equations:
2x+3y=13
y-3=-2x
Now isolate one variable in one of them. Let's use the second one since it will be faster to isolate y. Add three to both sides to get y on it's own so you get:
y=-2x+3
Now plug that value in for y in the first equation:
2x+3(-2x+3)=13
Solve for x:
2x+3(-2x+3)=13
2x-6x+9=13
-4x+9=13
-4x=4
x=-1
Now that we have the value of x, we can plug it into either equation and solve for y. Let's use the second one.
y-3=-2(-1)
y-3=2
y=5

So, we write as our answer:
x=-1
y=5