SOLUTION: Solve the system of eqations. x + 7y = -30 -2x + 6y = -40

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Question 241412: Solve the system of eqations.
x + 7y = -30
-2x + 6y = -40
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%28x%2B7y=-30%2C-2x%2B6y=-40%29


2%28x%2B7y%29=2%28-30%29 Multiply the both sides of the first equation by 2.


2x%2B14y=-60 Distribute and multiply.


So we have the new system of equations:
system%282x%2B14y=-60%2C-2x%2B6y=-40%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:


%282x%2B14y%29%2B%28-2x%2B6y%29=%28-60%29%2B%28-40%29


%282x%2B-2x%29%2B%2814y%2B6y%29=-60%2B-40 Group like terms.


0x%2B20y=-100 Combine like terms.


20y=-100 Simplify.


y=%28-100%29%2F%2820%29 Divide both sides by 20 to isolate y.


y=-5 Reduce.


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2x%2B14y=-60 Now go back to the first equation.


2x%2B14%28-5%29=-60 Plug in y=-5.


2x-70=-60 Multiply.


2x=-60%2B70 Add 70 to both sides.


2x=10 Combine like terms on the right side.


x=%2810%29%2F%282%29 Divide both sides by 2 to isolate x.


x=5 Reduce.


So the solutions are x=5 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 x%2B7y=-30 (red) and -2x%2B6y=-40 (green)