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)

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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) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x%2By=5%2Cx-y=-1%29


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


%28x%2By%29%2B%28x-1y%29=%285%29%2B%28-1%29


%281x%2B1x%29%2B%281y%2B-1y%29=5%2B-1 Group like terms.


2x%2B0y=4 Combine like terms.


2x=4 Simplify.


x=%284%29%2F%282%29 Divide both sides by 2 to isolate x.


x=2 Reduce.


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


x%2By=5 Now go back to the first equation.


2%2By=5 Plug in x=2.


2%2By=5 Multiply.


y=5-2 Subtract 2 from both sides.


y=3 Combine like terms on the right side.


So the solutions are x=2 and y=3.


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 x%2By=5 (red) and x-y=-1 (green)