SOLUTION: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. -3x + y = 4 2x – 3y = 9

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Question 207113: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.
-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%2C2x-3y=9%29


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


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


y=3x%2B4 Rearrange the terms and simplify.


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2x-3y=9 Move onto the second equation.


2x-3%283x%2B4%29=9 Now plug in y=3x%2B4.


2x-9x-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%28-7%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%28-3%29%2By=4 Plug in x=-3.


9%2By=4 Multiply.


y=4-9 Subtract 9 from both sides.


y=-5 Combine like terms on the right side.


So the solutions are x=-3 and y=-5.


which form the ordered pair (-3,-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-3y=9 (green)