SOLUTION: -2x – 8y = -42 -4x + 6y = -18

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Question 550512: -2x – 8y = -42
-4x + 6y = -18
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%28-2x-8y=-42%2C-4x%2B6y=-18%29


-2%28-2x-8y%29=-2%28-42%29 Multiply the both sides of the first equation by -2.


4x%2B16y=84 Distribute and multiply.


So we have the new system of equations:
system%284x%2B16y=84%2C-4x%2B6y=-18%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:


%284x%2B16y%29%2B%28-4x%2B6y%29=%2884%29%2B%28-18%29


%284x%2B-4x%29%2B%2816y%2B6y%29=84%2B-18 Group like terms.


0x%2B22y=66 Combine like terms.


22y=66 Simplify.


y=%2866%29%2F%2822%29 Divide both sides by 22 to isolate y.


y=3 Reduce.


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4x%2B16y=84 Now go back to the first equation.


4x%2B16%283%29=84 Plug in y=3.


4x%2B48=84 Multiply.


4x=84-48 Subtract 48 from both sides.


4x=36 Combine like terms on the right side.


x=%2836%29%2F%284%29 Divide both sides by 4 to isolate x.


x=9 Reduce.


So the solutions are x=9 and y=3.


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 -2x-8y=-42 (red) and -4x%2B6y=-18 (green)