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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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Now go back to the first equation.

Plug in .

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

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 (red) and (green)

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Add the two equations to eliminate x.

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