# How do you solve the system 7x + 2y = 2 and 6x - 2y = 8?

May 16, 2015

I notice that all the terms in the second equation are divisible by 2 and it will be easy to isolate $y$, so let's do that first.

$6 x - 2 y = 8$

Divide both sides by 2 to get

$3 x - y = 4$

Add $y$ to both sides to get

$3 x = 4 + y$

Subtract 8 from both sides to get

$y = 3 x - 4$

Now substitute this expression for $y$ into the first equation...

$2 = 7 x + 2 y$

$= 7 x + 2 \left(3 x - 4\right)$

$= 7 x + 6 x - 8$

$= 13 x - 8$

Add 8 to both sides to get

$13 x = 10$

Divide both sides by 13 to get

$x = \frac{10}{13}$

$y = 3 x - 4 = \frac{3 \times 10}{13} - 4$

$= \frac{30}{13} - \frac{4 \times 13}{13}$

$= \frac{30 - 52}{13}$

$= - \frac{22}{13}$