SOLUTION: Solve {{{system(4x-5y=-28,-9x-2y=10)}}}

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Question 191954: Solve
system%284x-5y=-28%2C-9x-2y=10%29
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%284x-5y=-28%2C-9x-2y=10%29


4x-5y=-28 Start with the first equation.


-5y=-28-4x Subtract 4x from both sides.


y=%28-28-4x%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=%28-28%29%2F%28-5%29-%284x%29%2F%28-5%29 Break up the fraction.


y=%284%2F5%29x%2B28%2F5 Reduce.


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-9x-2highlight%28%28%284%2F5%29x%2B28%2F5%29%29=10 Now plug in y=%284%2F5%29x%2B28%2F5 into the second equation.


-9x-%288%2F5%29x-56%2F5=10 Distribute.


Multiply EVERY term by the LCD 5 to clear any fractions.


-45x-8x-56=50 Multiply.


-53x-56=50 Combine like terms on the left side.


-53x=50%2B56 Add 56 to both sides.


-53x=106 Combine like terms on the right side.


x=%28106%29%2F%28-53%29 Divide both sides by -53 to isolate x.


x=-2 Reduce.


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Since we know that x=-2, we can use this to find y.


y=%284%2F5%29x%2B28%2F5 Go back to the first isolated equation


y=%284%2F5%29%28-2%29%2B28%2F5 Plug in x=-2.


y=-8%2F5%2B28%2F5 Multiply.


y=%28-8%2B28%29%2F5 Combine the fractions


y=20%2F5 Combine like terms.


y=4 Reduce.


So the solutions are x=-2 and y=4.


which form the ordered pair (-2,4)


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-5y=-28 (red) and -9x-2y=10 (green)