SOLUTION: Solve the following system for x and y. 3x - y = 7 x + 2y = -7

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Question 227682: Solve the following system for x and y.
3x - y = 7
x + 2y = -7
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-y=7%2Cx%2B2y=-7%29


2%283x-y%29=2%287%29 Multiply the both sides of the first equation by 2.


6x-2y=14 Distribute and multiply.


So we have the new system of equations:
system%286x-2y=14%2Cx%2B2y=-7%29


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


%286x-2y%29%2B%28x%2B2y%29=%2814%29%2B%28-7%29


%286x%2B1x%29%2B%28-2y%2B2y%29=14%2B-7 Group like terms.


7x%2B0y=7 Combine like terms.


7x=7 Simplify.


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


x=1 Reduce.


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6x-2y=14 Now go back to the first equation.


6%281%29-2y=14 Plug in x=1.


6-2y=14 Multiply.


-2y=14-6 Subtract 6 from both sides.


-2y=8 Combine like terms on the right side.


y=%288%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-4 Reduce.


So the solutions are x=1 and y=-4.


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-y=7 (red) and x%2B2y=-7 (green)