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

Jan 31, 2017

See the entire solution process below:

#### Explanation:

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

$- 6 x + y = - 8$

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

$0 + y = 6 x - 8$

$y = 6 x - 8$

Step 2) Substitute $6 x - 8$ for $y$ in the second equation and solve for $x$:

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

$- 3 x + 6 x - 8 = - 4$

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

$3 x - 8 = - 4$

$3 x - 8 + \textcolor{red}{8} = - 4 + \textcolor{red}{8}$

$3 x - 0 = 4$

$3 x = 4$

$\frac{3 x}{\textcolor{red}{3}} = \frac{4}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = \frac{4}{3}$

$x = \frac{4}{3}$

Step 3) Substitute $\frac{4}{3}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = \left(6 \times \frac{4}{3}\right) - 8$

$y = \frac{24}{3} - 8$

$y = 8 - 8$

$y = 0$

The solution is: $x = \frac{4}{3}$ and $y = 0$