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

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Question 175938: x-y=-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%28x-y=-1%2C2x-3y=-5%29


-3%28x-y%29=-3%28-1%29 Multiply the both sides of the first equation by -3.


-3x%2B3y=3 Distribute and multiply.


So we have the new system of equations:
system%28-3x%2B3y=3%2C2x-3y=-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:


%28-3x%2B3y%29%2B%282x-3y%29=%283%29%2B%28-5%29


%28-3x%2B2x%29%2B%283y%2B-3y%29=3%2B-5 Group like terms.


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


-x=-2 Simplify.


x=%28-2%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=2 Reduce.


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-3x%2B3y=3 Now go back to the first equation.


-3%282%29%2B3y=3 Plug in x=2.


-6%2B3y=3 Multiply.


3y=3%2B6 Add 6 to both sides.


3y=9 Combine like terms on the right side.


y=%289%29%2F%283%29 Divide both sides by 3 to isolate y.


y=3 Reduce.


So our answer is x=2 and y=3.


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-y=-1 (red) and 2x-3y=-5 (green)