# How do you solve the following system?:  -x+6y= - 2 , 5x - 2y= 3

May 7, 2017

Make the first equation $x = 6 y + 2$ and substitute into the second equation.

#### Explanation:

By adding x and 2 to both sides of the first equation, we get:
$x = 6 y + 2$
Now we substitute this expression of x into the second equation to get:
$5 \left(6 y + 2\right) - 2 y = 3$ which we can distribute the 5 on the left hand side to get:
$30 y + 10 - 2 y = 3$ which we combine the y-terms on the left hand side and subtract 10 from both sides:
$28 y = - 7$ by dividing both sides by 28, we get:
$y = - \frac{1}{4}$

By substituting this value of y into the $x = 6 y + 2$ equation, we get:
$x = 6 \left(- \frac{1}{4}\right) + 2$
$x = - \frac{3}{2} + 2$
$x = \frac{1}{2}$
Therefore, our answer is the coordinate point $\left(\frac{1}{2} , - \frac{1}{4}\right)$