SOLUTION: Solve the given system by use of substitution: 2x-5y=32 8x+62=y

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Question 202417: Solve the given system by use of substitution:

2x-5y=32
8x+62=y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I rearranged the second equation 8x%2B62=y to get y=8x%2B62



Start with the given system of equations:


system%282x-5y=32%2Cy=8x%2B62%29



2x-5y=32 Start with the first equation.


2x-5%288x%2B62%29=32 Plug in y=8x%2B62. Take note that the 'y' terms are gone and we can now solve for 'x'


2x-40x-310=32 Distribute.


-38x-310=32 Combine like terms on the left side.


-38x=32%2B310 Add 310 to both sides.


-38x=342 Combine like terms on the right side.


x=%28342%29%2F%28-38%29 Divide both sides by -38 to isolate x.


x=-9 Reduce.


-------------------------------------------


Since we know that x=-9, we can use this to find y.


2x-5y=32 Go back to the first equation.


2%28-9%29-5y=32 Plug in x=-9.


-18-5y=32 Multiply.


-5y=32%2B18 Add 18 to both sides.


-5y=50 Combine like terms on the right side.


y=%2850%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=-10 Reduce.


So the solutions are x=-9 and y=-10.


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x-5y=32 (red) and y=8x%2B62 (green)