SOLUTION: -7x-5y=-3 x-8y=-17

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Question 402977: -7x-5y=-3
x-8y=-17
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%28-7x-5y=-3%2Cx-8y=-17%29


7%28x-8y%29=7%28-17%29 Multiply the both sides of the second equation by 7.


7x-56y=-119 Distribute and multiply.


So we have the new system of equations:
system%28-7x-5y=-3%2C7x-56y=-119%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:


%28-7x-5y%29%2B%287x-56y%29=%28-3%29%2B%28-119%29


%28-7x%2B7x%29%2B%28-5y%2B-56y%29=-3%2B-119 Group like terms.


0x%2B-61y=-122 Combine like terms. Notice how the x terms cancel out.


-61y=-122 Simplify.


y=%28-122%29%2F%28-61%29 Divide both sides by -61 to isolate y.


y=2 Reduce.


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-7x-5y=-3 Now go back to the first equation.


-7x-5%282%29=-3 Plug in y=2.


-7x-10=-3 Multiply.


-7x=-3%2B10 Add 10 to both sides.


-7x=7 Combine like terms on the right side.


x=%287%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=-1 Reduce.


So our answer is 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 -7x-5y=-3 (red) and x-8y=-17 (green)