SOLUTION: 14x - 2y = 78 2x - 2y = 6

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Question 318610: 14x - 2y = 78
2x - 2y = 6
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%2814x-2y=78%2C2x-2y=6%29


-1%282x-2y%29=-1%286%29 Multiply the both sides of the second equation by -1.


-2x%2B2y=-6 Distribute and multiply.


So we have the new system of equations:
system%2814x-2y=78%2C-2x%2B2y=-6%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:


%2814x-2y%29%2B%28-2x%2B2y%29=%2878%29%2B%28-6%29


%2814x%2B-2x%29%2B%28-2y%2B2y%29=78%2B-6 Group like terms.


12x%2B0y=72 Combine like terms.


12x=72 Simplify.


x=%2872%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=6 Reduce.


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14x-2y=78 Now go back to the first equation.


14%286%29-2y=78 Plug in x=6.


84-2y=78 Multiply.


-2y=78-84 Subtract 84 from both sides.


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


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


y=3 Reduce.


So the solutions are x=6 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 14x-2y=78 (red) and 2x-2y=6 (green)