# How do you solve the following system?: 2x +13y =7, 8x -7y = 0

Mar 6, 2018

This can be solved by subtraction.

$x = \frac{49}{118}$

$y = \frac{28}{59}$

#### Explanation:

Multiplying both sides by 4,
$4 \left(2 x + 13 y\right) = 4 \left(7\right)$

$8 x + 52 y = 28$ --- (1)

$8 x - 7 y = 0$ --- (2)

Subtract the two equations:
(1) - (2): $8 x + 52 y - 8 x + 7 y = 28 - 0$

$59 y = 28$
$y = \frac{28}{59}$

$x = \frac{7 y}{8}$
$x = 7 \left(\frac{28}{59}\right) \cdot \left(\frac{1}{8}\right) = \frac{49}{118}$