SOLUTION: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent. 3y – x = 5 -x + 2y = -4

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Question 207121: Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.
3y – x = 5
-x + 2y = -4
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%283y-x=5%2C-x%2B2y=-4%29


3y-x=5 Start with the first equation.


3y=5%2Bx Add x to both sides.


y=%285%2Bx%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%281%2F3%29x%2B5%2F3 Rearrange the terms and simplify.


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-x%2B2y=-4 Move onto the second equation.


-x%2B2%28%281%2F3%29x%2B5%2F3%29=-4 Now plug in y=%281%2F3%29x%2B5%2F3.


-x%2B%282%2F3%29x%2B10%2F3=-4 Distribute.


3%28-x%2B%282%2Fcross%283%29%29x%2B10%2Fcross%283%29%29=3%28-4%29 Multiply both sides by the LCD 3 to clear any fractions.


-3x%2B2x%2B10=-12 Distribute and multiply.


-x%2B10=-12 Combine like terms on the left side.


-x=-12-10 Subtract 10 from both sides.


-x=-22 Combine like terms on the right side.


x=%28-22%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=22 Reduce.


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Since we know that x=22, we can use this to find y.


3y-x=5 Go back to the first equation.


3y-22=5 Plug in x=22.


3y=5%2B22 Add 22 to both sides.


3y=27 Combine like terms on the right side.


y=%2827%29%2F%283%29 Divide both sides by 3 to isolate y.


y=9 Reduce.


So the solutions are x=22 and y=9.


which form the ordered pair (22,9)


This means that the system is consistent and independent.