Solve by Substitution 8x-5y=-10 , -x-5y=11

Problem

{[8*x−5*y=−10],[−x−5*y=11])

Solution

1. Isolate the variable x in the second equation by adding 5*y to both sides and multiplying by −1

−x=5*y+11

x=−5*y−11

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

8*(−5*y−11)−5*y=−10

3. Distribute the 8 through the parentheses.

−40*y−88−5*y=−10

4. Combine the y terms.

−45*y−88=−10

5. Solve for y by adding 88 to both sides and then dividing by −45

−45*y=78

y=78/(−45)

y=−26/15

6. Substitute the value of y back into the expression for x

x=−5*(−26/15)−11

x=26/3−11

x=26/3−33/3

x=−7/3

Final Answer

(x,y)=(−7/3,−26/15)

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