# How do you solve the following system?: x +7y =53, x -9y = -56

Jan 5, 2016

$x = \frac{85}{16}$ and $y = \frac{109}{16}$

#### Explanation:

$x + 7 y = 53. \ldots \ldots \ldots \ldots \ldots \ldots \left(i\right)$
$x - 9 y = - 56. \ldots \ldots \ldots \ldots \ldots \ldots \left(i i\right)$

Subtract $\left(i i\right)$ from $\left(i\right)$

$\implies 16 y = 109$
$\implies y = \frac{109}{16}$

Put $y = \frac{109}{16}$ in $\left(i\right)$
$\implies x + 7 \left(\frac{109}{16}\right) = 53$
$\implies x + \frac{763}{16} = 53$
$\implies x = 53 - \frac{763}{16} = \frac{848 - 763}{16} = \frac{85}{16}$
$\implies x = \frac{85}{16}$