SOLUTION: solve by elimination method 7x+4y=15 4x-4y=-48 What is the solution of the system?

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Question 215093: solve by elimination method
7x+4y=15

4x-4y=-48
What is the solution of the system?
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%2B4y=15%2C4x-4y=-48%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%287x%2B4y%29%2B%284x-4y%29=%2815%29%2B%28-48%29


%287x%2B4x%29%2B%284y%2B-4y%29=15%2B-48 Group like terms.


11x%2B0y=-33 Combine like terms.


11x=-33 Simplify.


x=%28-33%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=-3 Reduce.


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7x%2B4y=15 Now go back to the first equation.


7%28-3%29%2B4y=15 Plug in x=-3.


-21%2B4y=15 Multiply.


4y=15%2B21 Add 21 to both sides.


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


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


y=9 Reduce.


So the solutions are x=-3 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%2B4y=15 (red) and 4x-4y=-48 (green)