# How do you solve the following system: 3x - 4y = -23, 5x+y=-7 ?

$x = - \frac{51}{23} , \setminus \setminus \setminus y = \frac{94}{23}$

#### Explanation:

Given equations

$3 x - 4 y = - 23 \setminus \ldots \ldots \left(1\right)$

$5 x + y = - 7 \setminus \ldots \ldots \ldots \left(2\right)$

Multiplying (2) by $4$ & adding to (1), we get

$3 x - 4 y + 4 \left(5 x + y\right) = - 23 + 4 \left(- 7\right)$

$23 x = - 51$

$x = - \frac{51}{23}$

setting the value of $x$ in (1), we get

$3 \left(- \frac{51}{23}\right) - 4 y = - 23$

$4 y = 23 - \frac{153}{23}$

$y = \setminus \frac{376}{23 \setminus \cdot 4}$

$y = \frac{94}{23}$

Hence the solution is $x = - \frac{51}{23} , \setminus \setminus \setminus y = \frac{94}{23}$