SOLUTION: 8x+9y=-2 -9x+y=69

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Question 200628: 8x+9y=-2
-9x+y=69
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%288x%2B9y=-2%2C-9x%2By=69%29


-9%28-9x%2By%29=-9%2869%29 Multiply the both sides of the second equation by -9.


81x-9y=-621 Distribute and multiply.


So we have the new system of equations:
system%288x%2B9y=-2%2C81x-9y=-621%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:


%288x%2B9y%29%2B%2881x-9y%29=%28-2%29%2B%28-621%29


%288x%2B81x%29%2B%289y%2B-9y%29=-2%2B-621 Group like terms.


89x%2B0y=-623 Combine like terms.


89x=-623 Simplify.


x=%28-623%29%2F%2889%29 Divide both sides by 89 to isolate x.


x=-7 Reduce.


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8x%2B9y=-2 Now go back to the first equation.


8%28-7%29%2B9y=-2 Plug in x=-7.


-56%2B9y=-2 Multiply.


9y=-2%2B56 Add 56 to both sides.


9y=54 Combine like terms on the right side.


y=%2854%29%2F%289%29 Divide both sides by 9 to isolate y.


y=6 Reduce.


So the solutions are x=-7 and y=6.


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 8x%2B9y=-2 (red) and -9x%2By=69 (green)