SOLUTION: the problem says solve each system of equations by substitution. -3x+y=-4 -2x+3y=9

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Question 223201: the problem says solve each system of equations by substitution.
-3x+y=-4
-2x+3y=9
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=-4%2C-2x%2B3y=9%29


-3x%2By=-4 Start with the first equation.


y=-4%2B3x Add 3x to both sides.


y=3x-4 Rearrange the terms.


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-2x%2B3%283x-4%29=9 Now plug in y=3x-4 into the second equation.


-2x%2B9x-12=9 Distribute.


7x-12=9 Combine like terms on the left side.


7x=9%2B12 Add 12 to both sides.


7x=21 Combine like terms on the right side.


x=%2821%29%2F%287%29 Divide both sides by 7 to isolate x.


x=3 Reduce.


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Since we know that x=3, we can use this to find y.


-3x%2By=-4 Go back to the first equation.


-3%283%29%2By=-4 Plug in x=3.


-9%2By=-4 Multiply.


y=-4%2B9 Add 9 to both sides.


y=5 Combine like terms on the right side.


So the answer is x=3 and y=5.


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=-4 (red) and -2x%2B3y=9 (green)