# How do solve the following linear system?: -2x + 3y = -19 , x - 3y = -6 ?

Mar 29, 2018

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#### Explanation:

$- 2 x + 3 y = - 19$
$x - 3 y = - 6$

We can use three methods to resolve. In this case we will use substitution

Express $x$ in second equation $x = - 6 + 3 y$. Now make the substitution in the first one

$- 2 \left(- 6 + 3 y\right) + 3 y = - 19$. Lets operate and transpose terms

$12 - 6 y + 3 y = - 19$;

$- 3 y = - 19 - 12 = - 21$. Then $y = - \frac{21}{-} 3 = 7$

Now lets find $x$ from the expresion $x = - 6 + 3 y = - 6 + 21 = 15$

The solution is $x = 15$ and $y = 7$