SOLUTION: Find the values of x and y that solve the following system of equations: -5x - 2y = 13 7x - 3y = 5

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Question 376372: Find the values of x and y that solve the following system of equations:
-5x - 2y = 13
7x - 3y = 5
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%28-5x-2y=13%2C7x-3y=5%29


7%28-5x-2y%29=7%2813%29 Multiply the both sides of the first equation by 7.


-35x-14y=91 Distribute and multiply.


5%287x-3y%29=5%285%29 Multiply the both sides of the second equation by 5.


35x-15y=25 Distribute and multiply.


So we have the new system of equations:
system%28-35x-14y=91%2C35x-15y=25%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:


%28-35x-14y%29%2B%2835x-15y%29=%2891%29%2B%2825%29


%28-35x%2B35x%29%2B%28-14y%2B-15y%29=91%2B25 Group like terms.


0x%2B-29y=116 Combine like terms.


-29y=116 Simplify.


y=%28116%29%2F%28-29%29 Divide both sides by -29 to isolate y.


y=-4 Reduce.


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-35x-14y=91 Now go back to the first equation.


-35x-14%28-4%29=91 Plug in y=-4.


-35x%2B56=91 Multiply.


-35x=91-56 Subtract 56 from both sides.


-35x=35 Combine like terms on the right side.


x=%2835%29%2F%28-35%29 Divide both sides by -35 to isolate x.


x=-1 Reduce.


So the solutions are x=-1 and y=-4.


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 -5x-2y=13 (red) and 7x-3y=5 (green)