# How do you solve the following system?: 7x -3y =11, -9x -24y = -7

Jun 24, 2018

#### Answer:

$x = \frac{19}{13}$ and $y = - \frac{10}{39}$

#### Explanation:

$8 \cdot \left(7 x - 3 y\right) - \left(- 9 x - 24 y\right) = 8 \cdot 11 - \left(- 7\right)$

$56 x - 24 y + 9 x + 24 y = 88 + 7$

$65 x = 95$, so $x = \frac{95}{65} = \frac{19}{13}$

Thus,

$7 \cdot \frac{19}{13} - 3 y = 11$

$\frac{133}{13} - 3 y = 11$

$- 3 y = \frac{10}{13}$ or $y = - \frac{10}{39}$

Jun 24, 2018

#### Answer:

$x = \frac{19}{13} , y = - \frac{10}{39}$

#### Explanation:

Multiplying the first equation by $- 8$ and adding to the second we get

$- 65 x = - 95$
so
$x = \frac{95}{65} = \frac{19}{13}$
plugging this in the first equation we get

$7 \cdot \frac{19}{13} - 3 y = 11$
$\frac{133}{13} - 11 = 3 y$

$\frac{133 - 143}{13} = 3 y$

$- \frac{10}{13} = 3 y$

so

$y = - \frac{10}{39}$