SOLUTION: how do I solve the system of equations: 2x+3y=40 and -2x+2y=20?

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Question 175694: how do I solve the system of equations: 2x+3y=40 and -2x+2y=20?
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%282x%2B3y=40%2C-2x%2B2y=20%29


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


%282x%2B3y%29%2B%28-2x%2B2y%29=%2840%29%2B%2820%29


%282x%2B-2x%29%2B%283y%2B2y%29=40%2B20 Group like terms.


0x%2B5y=60 Combine like terms. Notice how the x terms cancel out.


5y=60 Simplify.


y=%2860%29%2F%285%29 Divide both sides by 5 to isolate y.


y=12 Reduce.


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2x%2B3y=40 Now go back to the first equation.


2x%2B3%2812%29=40 Plug in y=12.


2x%2B36=40 Multiply.


2x=40-36 Subtract 36 from both sides.


2x=4 Combine like terms on the right side.


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


x=2 Reduce.


So our answer is x=2 and y=12.


Which form the ordered pair .


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%2B3y=40 (red) and -2x%2B2y=20 (green)