SOLUTION: Which ordered pair is a solution of the following system of equations? x+y=5 x-y=-1 1.(2,-3) 2.(2,3) 3.(3,-2) 4.(3,2)

Question 198021: Which ordered pair is a solution of the following system of equations?
x+y=5
x-y=-1
1.(2,-3)
2.(2,3)
3.(3,-2)
4.(3,2)

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.

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.

So the solutions are and .

Which form the ordered pair

. So the answer is the second choice.

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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