Question #8c1e4

Feb 5, 2017

$x = 3$ and $y = 1$

Explanation:

$- 3 x + 2 y = - 7$
$3 x + 3 y = 12$

From the first equation, derive a value for $3 x$.

$- 3 x + 2 y = - 7$

Multiply all terms with $- 1$.

$3 x - 2 y = 7$

Add $2 y$ to both sides.

$3 x = 7 + 2 y$

In the second equation, substitute $3 x$ with $\textcolor{red}{\left(7 + 2 y\right)}$.

$3 x + 3 y = 12$

$\textcolor{red}{\left(7 + 2 y\right)} + 3 y = 12$

Open the brackets and simplify.

$\textcolor{red}{7 + 2 y} + 3 y = 12$

$7 + 5 y = 12$

Subtract $7$ from each side.

$5 y = 5$

Divide both sides by $5$.

$y = 1$

In the second equation, substitute $y$ with $\textcolor{b l u e}{1}$.

$3 x + 3 y = 12$

$3 x + 3 \textcolor{b l u e}{\left(1\right)} = 12$

Open the brackets and simplify.

$3 x + 3 = 12$

Subtract $3$ from each side.

$3 x = 9$

Divide both sides by $3$.

$x = 3$