Solve by Substitution 8x+2y=-6 , -6x+y=17

Problem

{[8*x+2*y=−6],[−6*x+y=17])

Solution

1. Isolate the variable y in the second equation to prepare for substitution.

−6*x+y=17

y=6*x+17

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

8*x+2*(6*x+17)=−6

3. Distribute the constant into the parentheses.

8*x+12*x+34=−6

4. Combine the like terms involving x

20*x+34=−6

5. Isolate the x term by subtracting 34 from both sides.

20*x=−40

6. Solve for x by dividing both sides by 20.

x=−2

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

y=6*(−2)+17

y=−12+17

y=5

Final Answer

(x,y)=(−2,5)

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