SOLUTION: 9x + 11y = 86 9x – 2y = -5

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Question 550501: 9x + 11y = 86
9x – 2y = -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%289x%2B11y=86%2C9x-2y=-5%29


-1%289x%2B11y%29=-1%2886%29 Multiply the both sides of the first equation by -1.


-9x-11y=-86 Distribute and multiply.


So we have the new system of equations:
system%28-9x-11y=-86%2C9x-2y=-5%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:


%28-9x-11y%29%2B%289x-2y%29=%28-86%29%2B%28-5%29


%28-9x%2B9x%29%2B%28-11y%2B-2y%29=-86%2B-5 Group like terms.


0x%2B-13y=-91 Combine like terms.


-13y=-91 Simplify.


y=%28-91%29%2F%28-13%29 Divide both sides by -13 to isolate y.


y=7 Reduce.


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-9x-11y=-86 Now go back to the first equation.


-9x-11%287%29=-86 Plug in y=7.


-9x-77=-86 Multiply.


-9x=-86%2B77 Add 77 to both sides.


-9x=-9 Combine like terms on the right side.


x=%28-9%29%2F%28-9%29 Divide both sides by -9 to isolate x.


x=1 Reduce.


So the solutions are x=1 and y=7.


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 9x%2B11y=86 (red) and 9x-2y=-5 (green)