SOLUTION: x + 6y = -4 3x - 4y = 10 What are x and y?

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Question 178005: x + 6y = -4
3x - 4y = 10
What are x and y?
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%2B6y=-4%2C3x-4y=10%29


-3%28x%2B6y%29=-3%28-4%29 Multiply the both sides of the first equation by -3.


-3x-18y=12 Distribute and multiply.


So we have the new system of equations:
system%28-3x-18y=12%2C3x-4y=10%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:


%28-3x-18y%29%2B%283x-4y%29=%2812%29%2B%2810%29


%28-3x%2B3x%29%2B%28-18y%2B-4y%29=12%2B10 Group like terms.


0x%2B-22y=22 Combine like terms.


-22y=22 Simplify.


y=%2822%29%2F%28-22%29 Divide both sides by -22 to isolate y.


y=-1 Reduce.


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-3x-18y=12 Now go back to the first equation.


-3x-18%28-1%29=12 Plug in y=-1.


-3x%2B18=12 Multiply.


-3x=12-18 Subtract 18 from both sides.


-3x=-6 Combine like terms on the right side.


x=%28-6%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=2 Reduce.


So our answer is x=2 and y=-1.


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%2B6y=-4 (red) and 3x-4y=10 (green)