How do you solve the following system: 2x – 4y = 8, 2x-3y=-13?

1 Answer
DanT
Apr 13, 2018

x=-38, y=-21

Explanation:

One of the easiest ways to solve this is by realizing that when you subtract the equations, the x's cancel and you can solve for y.
2x-4y=8
-(2x-3y=-13)

You end up with:
-y=21, or y=-21

Then just plug it back into one of the equations for y, like this:
2x-4(-21)=8
Solve for x,
2x+84=8
2x=-76
x=-38

You could also solve by substitution.
Start by solving one of the equations for x or y- let's solve the first one for x:
2x-4y=8
2x=4y+8
x=2y+4
This is the same as x, right? So we can replace this for x in the second equation:
2(2y+4)-3y=-13
We've gotten rid of the x's, so we can solve for y:
4y+8-3y=-13
y=-21

Now just plug this y value into one of the equations and solve for x:
2x-4(-21)=8
2x+84=8
2x=-76
x=-38

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