Question

What is the solution to the system of linear equations?

-8x-7y=96
-3x+5y=-25

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Answer 1

`x = -5`

`y = -8`

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 = (3)/(5)x - (25)/(5)`

`y = (3)/(5)x - 5`

Substitute this value in the first equation

`-8x - 7((3)/(5)x - 5) = 96`

`-8x - 7*(3)/(5)x + 7 * 5 = 96`

`-8x - (21)/(5)x + 35 = 96`

Collect Like Terms

`-8x - (21)/(5)x = 96 - 35`

`(-61)/(5)x = 61`

`x = 61 * (-5)/(61)`

`x = -5`

Recall that

`y = (3)/(5)x - 5`

This gives

`y = (3)/(5) * -5 - 5`

`y = -3 - 5`

`y = -8`