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

Nov 4, 2015

$x = 1$
$y = 2$

#### 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

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

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.

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

Now let's add the two equations together!

$0 x - 7 y = - 14$

or just

$- 7 y = - 14$

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.

$x + 2 \left(2\right) = 5$

which simplifies to

$x + 4 = 5$

So we subtract 4 from both sides, and get

$x = 1$

Hope this helps!