SOLUTION: -7x+6y=-11 -5x-4y=17

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Question 678365: -7x+6y=-11
-5x-4y=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%2B6y=-11%2C-5x-4y=17%29


2%28-7x%2B6y%29=2%28-11%29 Multiply the both sides of the first equation by 2.


-14x%2B12y=-22 Distribute and multiply.


3%28-5x-4y%29=3%2817%29 Multiply the both sides of the second equation by 3.


-15x-12y=51 Distribute and multiply.


So we have the new system of equations:
system%28-14x%2B12y=-22%2C-15x-12y=51%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:


%28-14x%2B12y%29%2B%28-15x-12y%29=%28-22%29%2B%2851%29


%28-14x%2B-15x%29%2B%2812y%2B-12y%29=-22%2B51 Group like terms.


-29x%2B0y=29 Combine like terms.


-29x=29 Simplify.


x=%2829%29%2F%28-29%29 Divide both sides by -29 to isolate x.


x=-1 Reduce.


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-14x%2B12y=-22 Now go back to the first equation.


-14%28-1%29%2B12y=-22 Plug in x=-1.


14%2B12y=-22 Multiply.


12y=-22-14 Subtract 14 from both sides.


12y=-36 Combine like terms on the right side.


y=%28-36%29%2F%2812%29 Divide both sides by 12 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 -7x%2B6y=-11 (red) and -5x-4y=17 (green)