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