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

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

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

Start with the given system of equations:

Start with the first equation.

Plug in . Take note that the 'y' terms are gone and we can now solve for 'x'

Distribute.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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

Since we know that , we can use this to find .

Go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

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 (red) and (green)

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