# How do you solve the following system: -6x + y = -8, 2x+3y =4 ?

Mar 17, 2018

See a solution process below:

#### Explanation:

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

$- 6 x + y = - 8$

$- 6 x + \textcolor{red}{6 x} + y = - 8 + \textcolor{red}{6 x}$

$0 + y = - 8 + 6 x$

$y = - 8 + 6 x$

Step 2) Substitute $\left(- 8 + 6 x\right)$ for $y$ in the second equation and solve for $x$

$2 x + 3 y = 4$ becomes:

$2 x + 3 \left(- 8 + 6 x\right) = 4$

$2 x + \left(3 \times - 8\right) + \left(3 \times 6 x\right) = 4$

$2 x - 24 + 18 x = 4$

$2 x + 18 x - 24 = 4$

$\left(2 + 18\right) x - 24 = 4$

$20 x - 24 = 4$

$20 x - 24 + \textcolor{red}{24} = 4 + \textcolor{red}{24}$

$20 x - 0 = 28$

$20 x = 28$

$\frac{20 x}{\textcolor{red}{20}} = \frac{28}{\textcolor{red}{20}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{20}}} x}{\cancel{\textcolor{red}{20}}} = \frac{7}{5}$

$x = \frac{7}{5}$

Step 3) Substitute $\frac{7}{5}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = - 8 + 6 x$ becomes:

$y = - 8 + \left(6 \times \frac{7}{5}\right)$

$y = \left(\frac{5}{5} \times - 8\right) + \frac{42}{5}$

$y = - \frac{40}{5} + \frac{42}{5}$

$y = \frac{2}{5}$

The Solution Is:

$x = \frac{7}{5}$ and $y = \frac{2}{5}$

Or

$\left(\frac{7}{5} , \frac{2}{5}\right)$