SOLUTION: 5x - 3y = 8 -5x + y = 4

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Question 550363: 5x - 3y = 8
-5x + y = 4
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%285x-3y=8%2C-5x%2By=4%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%285x-3y%29%2B%28-5x%2By%29=%288%29%2B%284%29


%285x%2B-5x%29%2B%28-3y%2B1y%29=8%2B4 Group like terms.


0x%2B-2y=12 Combine like terms.


-2y=12 Simplify.


y=%2812%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-6 Reduce.


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5x-3y=8 Now go back to the first equation.


5x-3%28-6%29=8 Plug in y=-6.


5x%2B18=8 Multiply.


5x=8-18 Subtract 18 from both sides.


5x=-10 Combine like terms on the right side.


x=%28-10%29%2F%285%29 Divide both sides by 5 to isolate x.


x=-2 Reduce.


So the solutions are x=-2 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 5x-3y=8 (red) and -5x%2By=4 (green)