# How do solve the following linear system?:  9 x-6y =3 , 3x + y = -20 ?

Jun 19, 2018

See a solution process below:

#### Explanation:

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

$3 x + y = - 20$

$3 x - \textcolor{red}{3 x} + y = - \textcolor{red}{3 x} - 20$

$0 + y = - 3 x - 20$

$y = - 3 x - 20$

Step 2) Substitute $\left(- 3 x - 20\right)$ for $y$ in the first equation and solve for $x$:

$9 x - 6 y = 3$ becomes:

$9 x - 6 \left(- 3 x - 20\right) = 3$

$9 x - \left(6 \times - 3 x\right) - \left(6 \times - 20\right) = 3$

$9 x - \left(- 18 x\right) - \left(- 120\right) = 3$

$9 x + 18 x + 120 = 3$

$\left(9 + 18\right) x + 120 = 3$

$27 x + 120 = 3$

$27 x + 120 - \textcolor{red}{120} = 3 - \textcolor{red}{120}$

$27 x + 0 = - 117$

$27 x = - 117$

$\frac{27 x}{\textcolor{red}{27}} = - \frac{117}{\textcolor{red}{27}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{27}}} x}{\cancel{\textcolor{red}{27}}} = - \frac{9 \times 13}{\textcolor{red}{9 \times 3}}$

$x = - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} \times 13}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{9}}} \times 3}}$

$x = - \frac{13}{3}$

Step 3) Substitute $- \frac{13}{3}$ for $x$ in the solution to the second equation at the end of Step 1 and calculate $y$:

$y = - 3 x - 20$ becomes:

$y = - \left(3 \times - \frac{13}{3}\right) - 20$

$y = - \left(- 13\right) - 20$

$y = 13 - 20$

$y = - 7$

The Solution Is:

$x = - \frac{13}{3}$ and $y = - 7$

Or

$\left(- \frac{13}{3} , - 7\right)$