SOLUTION: Need to find he values of x and y that solves the system equation -4x + 5y = -10 5x - 4y = 8

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Question 211486: Need to find he values of x and y that solves the system equation
-4x + 5y = -10
5x - 4y = 8
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%28-4x%2B5y=-10%2C5x-4y=8%29


5%28-4x%2B5y%29=5%28-10%29 Multiply the both sides of the first equation by 5.


-20x%2B25y=-50 Distribute and multiply.


4%285x-4y%29=4%288%29 Multiply the both sides of the second equation by 4.


20x-16y=32 Distribute and multiply.


So we have the new system of equations:
system%28-20x%2B25y=-50%2C20x-16y=32%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:


%28-20x%2B25y%29%2B%2820x-16y%29=%28-50%29%2B%2832%29


%28-20x%2B20x%29%2B%2825y%2B-16y%29=-50%2B32 Group like terms.


0x%2B9y=-18 Combine like terms.


9y=-18 Simplify.


y=%28-18%29%2F%289%29 Divide both sides by 9 to isolate y.


y=-2 Reduce.


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-20x%2B25y=-50 Now go back to the first equation.


-20x%2B25%28-2%29=-50 Plug in y=-2.


-20x-50=-50 Multiply.


-20x=-50%2B50 Add 50 to both sides.


-20x=0 Combine like terms on the right side.


x=%280%29%2F%28-20%29 Divide both sides by -20 to isolate x.


x=0 Reduce.


So the solutions are x=0 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 -4x%2B5y=-10 (red) and 5x-4y=8 (green)