SOLUTION: -8x – 2y = -28 -3x + 5y = 47

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Question 550736: -8x – 2y = -28
-3x + 5y = 47
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-2y=-28%2C-3x%2B5y=47%29


3%28-8x-2y%29=3%28-28%29 Multiply the both sides of the first equation by 3.


-24x-6y=-84 Distribute and multiply.


-8%28-3x%2B5y%29=-8%2847%29 Multiply the both sides of the second equation by -8.


24x-40y=-376 Distribute and multiply.


So we have the new system of equations:
system%28-24x-6y=-84%2C24x-40y=-376%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:


%28-24x-6y%29%2B%2824x-40y%29=%28-84%29%2B%28-376%29


%28-24x%2B24x%29%2B%28-6y%2B-40y%29=-84%2B-376 Group like terms.


0x%2B-46y=-460 Combine like terms.


-46y=-460 Simplify.


y=%28-460%29%2F%28-46%29 Divide both sides by -46 to isolate y.


y=10 Reduce.


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-24x-6y=-84 Now go back to the first equation.


-24x-6%2810%29=-84 Plug in y=10.


-24x-60=-84 Multiply.


-24x=-84%2B60 Add 60 to both sides.


-24x=-24 Combine like terms on the right side.


x=%28-24%29%2F%28-24%29 Divide both sides by -24 to isolate x.


x=1 Reduce.


So the solutions are x=1 and y=10.


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-2y=-28 (red) and -3x%2B5y=47 (green)