How do you solve this system of equations: -3x - 5y = 4;- 5x - 4y = 24?

Apr 25, 2018

$x = - 8$, and $y = 4$.

Explanation:

Equation 1

$- 3 x - 5 y = 4$

Equation 2

$- 5 x - 4 y = 24$

I'm going to solve this by substitution.

First solve Equation 1 for x.

Equation 3

$x = - \frac{5 y + 4}{3}$

Next, substitute this expression for $x$ into Equation 2

Equation 4

$\frac{5 \left(5 y + 4\right)}{3} - 4 y = 24$

Now solve for $y$.

$25 y + 20 - 12 y = 72$

$13 y = 52$

$y = 4$

Now put this value for $y$ into Equation 3 to determine $x$.

$x = - \frac{5 \left(4\right) + 4}{3} = - 8$