Question

How do you solve x+2y=5 and 2x-3y=-4?

Answer 1

`x = 1`
`y = 2`

Explanation:

Ok. So prefer the elimination method, but you can do this with substitution as well.

First put the equations on top of each other

`x +2y= 5`
`2x-3y=-4`

Then find the variable that would be easiest to cancel out. I think it's `x` because you only have to modify one of the equations. Let's multiply the first equation by -2. This will allow us to cancel out the two `x`'s in the equations.

`-2x - 4y = -10`
`2x - 3y = -4`

Now let's add the two equations together!

`0x-7y = -14`

or just

`-7y = -14`

Now we simply divide by -7 to get `y`

`y = 2`

But wait! We're not done!

Plug `y` back into one of two equations to get `x`. I'll use the first equation again.

`x + 2(2) = 5`

which simplifies to

`x + 4 = 5`

So we subtract 4 from both sides, and get

`x = 1`

Hope this helps!