Question

What is the solution to the system of linear equations?

Answer 1

Answer:

$x = -5$

$y = -8$

Step-by-step explanation:

Given

$-8x - 7y = 96$

$-3x + 5y = -25$

Required

Determine x and y

Make y the subject  of formula in the second equation

$-3x + 5y = -25$

$5y = 3x - 25$

$y = \frac{3}{5}x - \frac{25}{5}$

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

Substitute this value in the first equation

$-8x - 7(\frac{3}{5}x - 5) = 96$

$-8x - 7*\frac{3}{5}x + 7 * 5 = 96$

$-8x - \frac{21}{5}x + 35 = 96$

Collect Like Terms

$-8x - \frac{21}{5}x = 96 - 35$

$\frac{-61}{5}x = 61$

$x = 61 * \frac{-5}{61}$

$x = -5$

Recall that

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

This gives

$y = \frac{3}{5} * -5 - 5$

$y = -3 - 5$

$y = -8$