# How do you solve x - 2y = -6 and -x + y = 2?

Jun 9, 2017

I got:
$x = 2$
$y = 4$

#### Explanation:

Have a look:

Jun 9, 2017

$x = 2 \mathmr{and} y = 4$

#### Explanation:

Make $x$ the subject of both equations:

$x = 2 y - 6 \text{ and } x = y - 2$

The value of $x$ is the same, so if:

$\text{ } x = x$ then:
$2 y - 6 = y - 2 \text{ } \leftarrow$ solve for $y$

$2 y - y = - 2 + 6$

$y = 4$

$x = 2 \left(4\right) - 6$

$x = 8 - 6$

$x = 2$

Jun 9, 2017

$x = 2$
$y = 4$

#### Explanation:

We could also solve this problem using substitution.

Solve the 1st equation for $x$:

$x - 2 y = - 6$

$x = 2 y - 6$

Substitute the above into the 2nd equation and solve for $y$:

$- x + y = 2$

$- \left(2 y - 6\right) + y = 2$

$- 2 y + 6 + y = 2$

$- y = - 4$

$y = 4$

Substitute $y$ into the 1st equation and solve for $x$:

$x - 2 y = - 6$

$x - 2 \left(4\right) = - 6$

$x = 2$