SOLUTION: 7x+2y=24 8x+2y=30

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Question 255417: 7x+2y=24
8x+2y=30
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%287x%2B2y=24%2C8x%2B2y=30%29


-1%288x%2B2y%29=-1%2830%29 Multiply the both sides of the second equation by -1.


-8x-2y=-30 Distribute and multiply.


So we have the new system of equations:
system%287x%2B2y=24%2C-8x-2y=-30%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:


%287x%2B2y%29%2B%28-8x-2y%29=%2824%29%2B%28-30%29


%287x%2B-8x%29%2B%282y%2B-2y%29=24%2B-30 Group like terms.


-x%2B0y=-6 Combine like terms.


-x=-6 Simplify.


x=%28-6%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=6 Reduce.


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7x%2B2y=24 Now go back to the first equation.


7%286%29%2B2y=24 Plug in x=6.


42%2B2y=24 Multiply.


2y=24-42 Subtract 42 from both sides.


2y=-18 Combine like terms on the right side.


y=%28-18%29%2F%282%29 Divide both sides by 2 to isolate y.


y=-9 Reduce.


So the solutions are x=6 and y=-9.


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 7x%2B2y=24 (red) and 8x%2B2y=30 (green)