# How do you solve using elimination of 2x - 3y = 12 and 3x + 5y = -1?

Jun 11, 2018

$x = 3$
$y = - 2$

#### Explanation:

On paper you should line the equations up, one below the other:

$2 x - 3 y = 12$
$3 x + 5 y = - 1$

In elimination, you have to find the least common multiple between one of the variables. I prefer to eliminate $x$ and solve for $y$ first and so the least common multiple between $2 x$ and $3 x$ is $6 x$.

You’ll have to multiply $2 x - 3 y = 12$ by $3$ and
$3 x + 5 y = - 1$ by $2$

$6 x - 9 y = - 36$
$6 x + 10 y = - 2$

Now you have to combine the equations by subtracting the bottom equation from the top:

$- 19 y = 38$
Notice that we added $2$ to $36$ because if you try to subtract a negative, the negative turns positive.

Now to isolate $y$, divide both sides by $- 19$

$y = - 2$

Now that we found $y$, let’s subtitute it into either equation to find $x$. I’ll choose the top equation:

$2 x - 3 \left(- 2\right) = 12$
$2 x + 6 = 12$

Now, we subtract $6$ from both sides in an attempt to isolate $x$.

$2 x = 6$

Divide both sides by $2$

$x = 3$

And there you go!

$y = - 2$ and $x = 3$

Hope this helps!