SOLUTION: Please help: Find the values of x and y that solve the following system of equations: 5x + 7y = -1 7x + 3y = -15

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Question 299401: Please help: Find the values of x and y that solve the following system of equations:
5x + 7y = -1
7x + 3y = -15
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%285x%2B7y=-1%2C7x%2B3y=-15%29


3%285x%2B7y%29=3%28-1%29 Multiply the both sides of the first equation by 3.


15x%2B21y=-3 Distribute and multiply.


-7%287x%2B3y%29=-7%28-15%29 Multiply the both sides of the second equation by -7.


-49x-21y=105 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B21y=-3%2C-49x-21y=105%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:


%2815x%2B21y%29%2B%28-49x-21y%29=%28-3%29%2B%28105%29


%2815x%2B-49x%29%2B%2821y%2B-21y%29=-3%2B105 Group like terms.


-34x%2B0y=102 Combine like terms.


-34x=102 Simplify.


x=%28102%29%2F%28-34%29 Divide both sides by -34 to isolate x.


x=-3 Reduce.


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15x%2B21y=-3 Now go back to the first equation.


15%28-3%29%2B21y=-3 Plug in x=-3.


-45%2B21y=-3 Multiply.


21y=-3%2B45 Add 45 to both sides.


21y=42 Combine like terms on the right side.


y=%2842%29%2F%2821%29 Divide both sides by 21 to isolate y.


y=2 Reduce.


So the solutions are x=-3 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 5x%2B7y=-1 (red) and 7x%2B3y=-15 (green)