Solve by Substitution 2x+7y=-16 , -7x-8y=23

Problem

{[2*x+7*y=−16],[−7*x−8*y=23])

Solution

1. Isolate the variable x in the first equation by subtracting 7*y from both sides and then dividing by 2

2*x=−16−7*y

x=−8−3.5*y

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

−7*(−8−3.5*y)−8*y=23

3. Distribute the −7 into the parentheses.

56+24.5*y−8*y=23

4. Combine the y terms and subtract 56 from both sides to solve for y

16.5*y=−33

y=−2

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

x=−8−3.5*(−2)

x=−8+7

x=−1

Final Answer

(x,y)=(−1,−2)

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