SOLUTION: 2x +5y = 17 6x - 5y = -9

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Question 585640: 2x +5y = 17
6x - 5y = -9
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%2B5y=17%2C6x-5y=-9%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%2B5y%29%2B%286x-5y%29=%2817%29%2B%28-9%29


%282x%2B6x%29%2B%285y%2B-5y%29=17%2B-9 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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2x%2B5y=17 Now go back to the first equation.


2%281%29%2B5y=17 Plug in x=1.


2%2B5y=17 Multiply.


5y=17-2 Subtract 2 from both sides.


5y=15 Combine like terms on the right side.


y=%2815%29%2F%285%29 Divide both sides by 5 to isolate y.


y=3 Reduce.


So the solutions are x=1 and y=3.


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%2B5y=17 (red) and 6x-5y=-9 (green)



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