SOLUTION: -x+4y=-11 2x+4y=-2

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Question 200121: -x+4y=-11
2x+4y=-2
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%28-x%2B4y=-11%2C2x%2B4y=-2%29


2%28-x%2B4y%29=2%28-11%29 Multiply the both sides of the first equation by 2.


-2x%2B8y=-22 Distribute and multiply.


So we have the new system of equations:
system%28-2x%2B8y=-22%2C2x%2B4y=-2%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:


%28-2x%2B8y%29%2B%282x%2B4y%29=%28-22%29%2B%28-2%29


%28-2x%2B2x%29%2B%288y%2B4y%29=-22%2B-2 Group like terms.


0x%2B12y=-24 Combine like terms.


12y=-24 Simplify.


y=%28-24%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=-2 Reduce.


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-2x%2B8y=-22 Now go back to the first equation.


-2x%2B8%28-2%29=-22 Plug in y=-2.


-2x-16=-22 Multiply.


-2x=-22%2B16 Add 16 to both sides.


-2x=-6 Combine like terms on the right side.


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


x=3 Reduce.


So the solutions are x=3 and y=-2.


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%2B4y=-11 (red) and 2x%2B4y=-2 (green)