# How do you solve the system of equations 6x - 3y = 12 and - 5x + 3y = - 5?

Mar 11, 2017

$x = 7 , y = 10$

#### Explanation:

We have that:

$- 5 x + 3 y = - 5$
$6 x - 3 y = 12$

We can easily solve by eliminating the $y$ value. Add both equations together to get:

$\left(- 5 x + 3 y\right) + \left(6 x - 3 y\right) = - 5 + 12$

Simplifying leaves us with:

$x = 7$

We can now substitute our value of $x$ back into either of these equation to get $y$. We will chose the top one:

$- 5 x + 3 y = - 5$

$x = 7 \to - 5 \left(7\right) + 3 y = - 5$

$- 35 + 3 y = - 5$

So:
$3 y = 30 \to y = 10$

Hence $x = 7 , y = 10$

We can check the solution by substituting into the other equation, so:

$6 x - 3 y = 12$
$x = 7 , y = 10 \to 6 \left(7\right) - 3 \left(10\right) = 42 - 30 = 12$

As expected.