SOLUTION: how to solve 2x-5y = 9 -3x+y=-7

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Question 550712: how to solve 2x-5y = 9
-3x+y=-7
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-5y=9%2C-3x%2By=-7%29


5%28-3x%2By%29=5%28-7%29 Multiply the both sides of the second equation by 5.


-15x%2B5y=-35 Distribute and multiply.


So we have the new system of equations:
system%282x-5y=9%2C-15x%2B5y=-35%29


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


%282x-5y%29%2B%28-15x%2B5y%29=%289%29%2B%28-35%29


%282x%2B-15x%29%2B%28-5y%2B5y%29=9%2B-35 Group like terms.


-13x%2B0y=-26 Combine like terms.


-13x=-26 Simplify.


x=%28-26%29%2F%28-13%29 Divide both sides by -13 to isolate x.


x=2 Reduce.


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2x-5y=9 Now go back to the first equation.


2%282%29-5y=9 Plug in x=2.


4-5y=9 Multiply.


-5y=9-4 Subtract 4 from both sides.


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


y=%285%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=-1 Reduce.


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


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-5y=9 (red) and -3x%2By=-7 (green)