How do you solve 6x - 2y = -16 and 4x + 4y = -32 ?

Aug 10, 2016

$x = - 4$
$y = - 4$-

Explanation:

$6 x - 2 y = - 16$ and
$4 x + 4 y = - 32$
or
$2 x + 2 y = - 16$
or
$x + y = - 8$
Adding up the equations $6 x - 2 y = - 16$ and $2 x + 2 y = - 16$
We get
$6 x - 2 y + 2 x + 2 y = - 16 - 16$
or
$8 x = - 32$
or
$x = - \frac{32}{8}$
or
$x = - 4$--------------------Ans $1$
By putting the value $x = - 4$ in the equation $x + y = - 8$
We get
$- 4 + y = - 8$
or
$y = 4 - 8$
or
$y = - 4$-----------------------Ans $2$

Aug 10, 2016

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

Explanation:

Neither of the equations is in the simplest form. Let's do that first and see what we end up with.

$6 x - 2 y = - 16 \text{ "(div 2)" } \Rightarrow 3 x - y = - 8 \ldots \ldots \ldots . A$

$4 x + 4 y = - 32 \text{ " (div 4) " } \Rightarrow x + y = - 8 \ldots \ldots \ldots \ldots B$

We notice that $+ y \mathmr{and} - y$ are additive inverses which will add to 0 if we add equations $A \mathmr{and} B$ together.

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 3 x - y = - 8 \ldots \ldots \ldots . A$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots . .} x + y = - 8 \ldots \ldots \ldots \ldots B$

$A + B \textcolor{w h i t e}{\ldots \ldots \ldots} 4 x = - 16$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots} x = - 4$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots . .} y = - 4$