Answer:
[tex]x = -5[/tex]
[tex]y = -8[/tex]
Step-by-step explanation:
Given
[tex]-8x - 7y = 96[/tex]
[tex]-3x + 5y = -25[/tex]
Required
Determine x and y
Make y the subject of formula in the second equation
[tex]-3x + 5y = -25[/tex]
[tex]5y = 3x - 25[/tex]
[tex]y = \frac{3}{5}x - \frac{25}{5}[/tex]
[tex]y = \frac{3}{5}x - 5[/tex]
Substitute this value in the first equation
[tex]-8x - 7(\frac{3}{5}x - 5) = 96[/tex]
[tex]-8x - 7*\frac{3}{5}x + 7 * 5 = 96[/tex]
[tex]-8x - \frac{21}{5}x + 35 = 96[/tex]
Collect Like Terms
[tex]-8x - \frac{21}{5}x = 96 - 35[/tex]
[tex]\frac{-61}{5}x = 61[/tex]
[tex]x = 61 * \frac{-5}{61}[/tex]
[tex]x = -5[/tex]
Recall that
[tex]y = \frac{3}{5}x - 5[/tex]
This gives
[tex]y = \frac{3}{5} * -5 - 5[/tex]
[tex]y = -3 - 5[/tex]
[tex]y = -8[/tex]
