# How do you solve the system of linear equations 5x - 4y = 7, 2y + 6x = 22?

Dec 5, 2016

$x = 3$ and $y = 2$.

#### Explanation:

$5 x - 4 y = 7$
$2 y + 6 x = 22$

From the second equation, we can determine a value for $4 y$.

$2 y + 6 x = 22$

Multiply all terms by $2$.

$4 y + 12 x = 44$

Subtract $12 x$ from both sides.

$4 y = 44 - 12 x$

In the first equation, replace $4 y$ with $\textcolor{red}{\left(44 - 12 x\right)}$.

$5 x - 4 y = 7$

$5 x - \textcolor{red}{\left(44 - 12 x\right)} = 7$

Open the brackets and simplify. The product of two negatives i a positive.

$5 x - \textcolor{red}{44 + 12 x} = 7$

$17 x - 44 = 7$

Add $44$ to both sides.

$17 x = 51$

Divide both sides by $17$.

$x = 3$

In the second equation, substitute $x$ with $3$.

$2 y + 6 x = 22$

$2 y + \left(6 \times 3\right) = 22$

$2 y + 18 = 22$

Subtract $18$ from both sides.

$2 y = 4$

Divide both sides by $2$.

$y = 2$