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

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Question 254869: 6x-2y=8
-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%286x-2y=8%2C-4x%2B6y=18%29


3%286x-2y%29=3%288%29 Multiply the both sides of the first equation by 3.


18x-6y=24 Distribute and multiply.


So we have the new system of equations:
system%2818x-6y=24%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:


%2818x-6y%29%2B%28-4x%2B6y%29=%2824%29%2B%2818%29


%2818x%2B-4x%29%2B%28-6y%2B6y%29=24%2B18 Group like terms.


14x%2B0y=42 Combine like terms.


14x=42 Simplify.


x=%2842%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=3 Reduce.


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18x-6y=24 Now go back to the first equation.


18%283%29-6y=24 Plug in x=3.


54-6y=24 Multiply.


-6y=24-54 Subtract 54 from both sides.


-6y=-30 Combine like terms on the right side.


y=%28-30%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=5 Reduce.


So the solutions are x=3 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 6x-2y=8 (red) and -4x%2B6y=18 (green)