SOLUTION: -x-5y=-1 2x+3y=-5

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Question 166281: -x-5y=-1
2x+3y=-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%28-x-5y=-1%2C2x%2B3y=-5%29


2%28-x-5y%29=2%28-1%29 Multiply the both sides of the first equation by 2.


-2x-10y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-2x-10y=-2%2C2x%2B3y=-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:


%28-2x-10y%29%2B%282x%2B3y%29=%28-2%29%2B%28-5%29


%28-2x%2B2x%29%2B%28-10y%2B3y%29=-2%2B-5 Group like terms.


0x%2B-7y=-7 Combine like terms. Notice how the x terms cancel out.


-7y=-7 Simplify.


y=%28-7%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=1 Reduce.


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-2x-10y=-2 Now go back to the first equation.


-2x-10%281%29=-2 Plug in y=1.


-2x-10=-2 Multiply.


-2x=-2%2B10 Add 10 to both sides.


-2x=8 Combine like terms on the right side.


x=%288%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=-4 Reduce.


So our answer is x=-4 and y=1.


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 -x-5y=-1 (red) and 2x%2B3y=-5 (green)