SOLUTION: Please help me solve this equation: 3x+2y=7 5x-2y=1

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Question 200985: Please help me solve this equation: 3x+2y=7
5x-2y=1
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%283x%2B2y=7%2C5x-2y=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:


%283x%2B2y%29%2B%285x-2y%29=%287%29%2B%281%29


%283x%2B5x%29%2B%282y-2y%29=7%2B1 Group like terms.


8x%2B0y=8 Combine like terms.


8x=8 Simplify.


x=%288%29%2F%288%29 Divide both sides by 8 to isolate x.


x=1 Reduce.


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3x%2B2y=7 Now go back to the first equation.


3%281%29%2B2y=7 Plug in x=1.


3%2B2y=7 Multiply.


2y=7-3 Subtract 3 from both sides.


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


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


y=2 Reduce.


So the solutions are x=1 and y=2.


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 3x%2B2y=7 (red) and 5x-2y=1 (green)