# How do you solve the following system?: 17x +19y =14, -7x +15y = -22

##### 1 Answer
Oct 27, 2017

$y = - 0.71$
$x = 1.62$

#### Explanation:

$17 x + 19 y = 14$
$- 7 x + 15 y = - 22$

Using one of the equations, make either $x$ or $y$ the subject.

$17 x + 19 y = 14 \to 17 x = 14 - 19 y$

$x = \frac{14 - 19 y}{17}$

Then inject this in place of the $x$ in the second equation to calculate $y$.

$- 7 \left(\frac{14 - 19 y}{17}\right) + 15 y = - 22$

Multiply out the bracket.

$\frac{- 98 + 133 y}{17} + 15 y = - 22$

Multiply everything by $17$ to get rid of fractions.

$- 98 + 133 y + 255 y = - 374$

Now calculate $y$.

$388 y = - 276$

$y = - \frac{276}{388}$

$y = - 0.71$

Now substitute the calculated $y$ value into the rearranged equation to calculate $x$.

$x = \frac{14 - 19 \left(- 0.71\right)}{17}$

$x = 1.62$