SOLUTION: -3x+y=3 and 2x-y=-1 what is the solution

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Question 203073: -3x+y=3 and 2x-y=-1
what is the solution
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%28-3x%2By=3%2C2x-y=-1%29


-3x%2By=3 Start with the first equation.


y=3%2B3x Add 3x to both sides.


y=3x%2B3 Rearrange the terms and simplify.


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2x-y=-1 Move onto the second equation.


2x-%283x%2B3%29=-1 Now plug in y=3x%2B3.


2x-3x-3=-1 Distribute.


-x-3=-1 Combine like terms on the left side.


-x=-1%2B3 Add 3 to both sides.


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


x=%282%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-2 Reduce.


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


-3x%2By=3 Go back to the first equation.


-3%28-2%29%2By=3 Plug in x=-2.


6%2By=3 Multiply.


y=3-6 Subtract 6 from both sides.


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


So the solutions are x=-2 and y=-3.


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