SOLUTION: Please solve each system -5x + 2y = 9 -3x + 8y = -15

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Question 374762: Please solve each system
-5x + 2y = 9
-3x + 8y = -15
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%28-5x%2B2y=9%2C-3x%2B8y=-15%29


-4%28-5x%2B2y%29=-4%289%29 Multiply the both sides of the first equation by -4.


20x-8y=-36 Distribute and multiply.


So we have the new system of equations:
system%2820x-8y=-36%2C-3x%2B8y=-15%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:


%2820x-8y%29%2B%28-3x%2B8y%29=%28-36%29%2B%28-15%29


%2820x%2B-3x%29%2B%28-8y%2B8y%29=-36%2B-15 Group like terms.


17x%2B0y=-51 Combine like terms.


17x=-51 Simplify.


x=%28-51%29%2F%2817%29 Divide both sides by 17 to isolate x.


x=-3 Reduce.


------------------------------------------------------------------


20x-8y=-36 Now go back to the first equation.


20%28-3%29-8y=-36 Plug in x=-3.


-60-8y=-36 Multiply.


-8y=-36%2B60 Add 60 to both sides.


-8y=24 Combine like terms on the right side.


y=%2824%29%2F%28-8%29 Divide both sides by -8 to isolate y.


y=-3 Reduce.


So the solutions are x=-3 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 -5x%2B2y=9 (red) and -3x%2B8y=-15 (green)



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim