Question

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

Answer 1

`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`