# How do you solve the following system: -3x + y = -4, 6y + 4x = 12 ?

Aug 27, 2017

See a solution process below: $\left(\frac{18}{11} , \frac{10}{11}\right)$

#### Explanation:

Step 1) Solve the first equation for $y$:

$- 3 x + y = - 4$

$\textcolor{red}{3 x} - 3 x + y = \textcolor{red}{3 x} - 4$

$0 + y = 3 x - 4$

$y = 3 x - 4$

Step 2) Substitute $\left(3 x - 4\right)$ for $y$ in the second equation and solve for $x$:

$6 y + 4 x = 12$ becomes:

$6 \left(3 x - 4\right) + 4 x = 12$

$\left(6 \cdot 3 x\right) - \left(6 \cdot 4\right) + 4 x = 12$

$18 x - 24 + 4 x = 12$

$18 x + 4 x - 24 = 12$

$\left(18 + 4\right) x - 24 = 12$

$22 x - 24 = 12$

$22 x - 24 + \textcolor{red}{24} = 12 + \textcolor{red}{24}$

$22 x - 0 = 36$

$22 x = 36$

$\frac{22 x}{\textcolor{red}{22}} = \frac{36}{\textcolor{red}{22}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{22}}} x}{\cancel{\textcolor{red}{22}}} = \frac{2 \times 18}{\textcolor{red}{2 \times 11}}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 18}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}} \times 11}}$

$x = \frac{18}{11}$

Step 3) Substitute $\frac{18}{11}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = 3 x - 4$ becomes:

$y = \left(3 \times \frac{18}{11}\right) - 4$

$y = \frac{54}{11} - 4$

$y = \frac{54}{11} - \left(\frac{11}{11} \times 4\right)$

$y = \frac{54}{11} - \frac{44}{11}$

$y = \frac{10}{11}$

The Solution Is: $x = \frac{18}{11}$ and $y = \frac{10}{11}$ or $\left(\frac{18}{11} , \frac{10}{11}\right)$