# How do solve the following linear system?:  2x - 3y = 1 , 3x + y = -20 ?

Jul 13, 2016

$x = - \frac{59}{11} \text{ and } y = - 3 \frac{10}{11}$

#### Explanation:

The second equation contains a single $y$ term, so it is easy to transpose this to give: $y = - 3 x - 20$

We now have an expression for $y$ in terms of x and can substitute that into the other equation:

2x-3color(magenta)y =1 " and "color(magenta)(y = -3x -20

$2 x - 3 \left(\textcolor{m a \ge n t a}{- 3 x - 20}\right) = 1$
$2 x + 9 x + 60 = 1$

$11 x = - 59$

$\textcolor{b l u e}{x = - \frac{59}{11}} \text{ }$But $y = - 3 \textcolor{b l u e}{x} - 20$
$y = - 3 \left(\textcolor{b l u e}{\frac{- 59}{11}}\right) - 20$

$y = - 3 \frac{10}{11}$