SOLUTION: What is the vaule of the Y variable in the solution to the following system of equations? 3x+y=14 -3x+2y=1

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Question 318591: What is the vaule of the Y variable in the solution to the following system of equations?
3x+y=14
-3x+2y=1
Found 2 solutions by jim_thompson5910, Fombitz:
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%283x%2By=14%2C-3x%2B2y=1%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%283x%2By%29%2B%28-3x%2B2y%29=%2814%29%2B%281%29


%283x%2B-3x%29%2B%281y%2B2y%29=14%2B1 Group like terms.


0x%2B3y=15 Combine like terms.


3y=15 Simplify.


y=%2815%29%2F%283%29 Divide both sides by 3 to isolate y.


y=5 Reduce.


------------------------------------------------------------------


3x%2By=14 Now go back to the first equation.


3x%2B5=14 Plug in y=5.


3x=14-5 Subtract 5 from both sides.


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


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


x=3 Reduce.


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


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 3x%2By=14 (red) and -3x%2B2y=1 (green)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Add the two equations to eliminate x.
3x%2By-3x%2B2y=14%2B1
3y=15
highlight%28y=5%29