# How do you solve by substitution 3x + 2y = 6 and x + 2y = -6?

Jun 13, 2015

$x = 6$
$y = - 6$

#### Explanation:

Try this:

Jun 13, 2015

$x = 6$
$y = - 6$

#### Explanation:

To solve a system by substitution, you need to replace one unknown by a function of the other, using one of the equations.

Example:
$x + 2 y = - 6$
becomes
$x = - 2 y - 6$

Then, in the other equation, you replace $x$ with its $y$-depending expression:

$3 x + 2 y = 6$
becomes
$2 y - 6 y - 18 = 6$
$\rightarrow - 4 y = 24$
$\rightarrow y = - 6$

Now that you have the value of $y$, you can find the value of $x$:

$x = - 2 y - 6$
becomes
$x = - 2 \cdot \left(- 6\right) - 6$
$\rightarrow x = 12 - 6 = 6$