SOLUTION: -8x – 4y = -68 x + 3y = 16

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Question 550713: -8x – 4y = -68
x + 3y = 16
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%28-8x-4y=-68%2Cx%2B3y=16%29


8%28x%2B3y%29=8%2816%29 Multiply the both sides of the second equation by 8.


8x%2B24y=128 Distribute and multiply.


So we have the new system of equations:
system%28-8x-4y=-68%2C8x%2B24y=128%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:


%28-8x-4y%29%2B%288x%2B24y%29=%28-68%29%2B%28128%29


%28-8x%2B8x%29%2B%28-4y%2B24y%29=-68%2B128 Group like terms.


0x%2B20y=60 Combine like terms.


20y=60 Simplify.


y=%2860%29%2F%2820%29 Divide both sides by 20 to isolate y.


y=3 Reduce.


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-8x-4y=-68 Now go back to the first equation.


-8x-4%283%29=-68 Plug in y=3.


-8x-12=-68 Multiply.


-8x=-68%2B12 Add 12 to both sides.


-8x=-56 Combine like terms on the right side.


x=%28-56%29%2F%28-8%29 Divide both sides by -8 to isolate x.


x=7 Reduce.


So the solutions are x=7 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 -8x-4y=-68 (red) and x%2B3y=16 (green)