# How do you solve the following linear system: -7x - 5y =4, -x + y = 21 ?

Nov 14, 2015

$x = \frac{101}{12}$,

$y = \frac{353}{12}$.

#### Explanation:

$- 7 x - 5 y = 4$,
$- x + y = 21$.

There are three ways of solving these problems. I'll choose substitution, as I find it easier. Let's start. First of all, we leave $x$ or $y$ alone in any of the $2$ equations. So,
$- x + y = 21$,
$y = x + 21$.

We now substitute this into the other equation:
$- 7 x - 5 \left(x + 21\right) = 4$,
$- 7 x - 5 x + 105 = 4$,
$- 12 x = - 101$, Which we can write as:
$12 x = 101$
$x = \frac{101}{12}$.

We now substitute this into any of the equation. I'll choose the second one:

$- \frac{101}{12} + y = 21$,
$y = 21 + \frac{101}{12}$
$y = \frac{353}{12}$.