Solve by Substitution x-y=4 , 7x+8y=-107

Problem

{[x−y=4],[7*x+8*y=−107])

Solution

1. Isolate a variable in the first equation by adding y to both sides.

x=y+4

2. Substitute the expression for x into the second equation.

7*(y+4)+8*y=−107

3. Distribute the 7 into the parentheses.

7*y+28+8*y=−107

4. Combine the like terms 7*y and 8*y

15*y+28=−107

5. Subtract 28 from both sides of the equation.

15*y=−135

6. Divide by 15 to solve for y

y=−9

7. Substitute the value of y back into the isolated equation for x

x=−9+4

8. Simplify to find the value of x

x=−5

Final Answer

(x,y)=(−5,−9)

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