SOLUTION: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks Solve the system of equations x+2y=1 3x-2y=11 My answer is (3,-1) Thank you

Question 218289: I need to know if my answer is correct for the following: If it isn't, I need to know why. thanks
Solve the system of equations
x+2y=1
3x-2y=11
My answer is (3,-1)
Thank you very much!
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms. Notice how the y terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

Which form the ordered pair . Good job. As a check, simply plug in and and you should get two identities.

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)

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Spot on.
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