SOLUTION: solve and graph this system of equations 3x - 5y = -9 5x - 6y = -8

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Question 198956: solve and graph this system of equations
3x - 5y = -9
5x - 6y = -8
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%283x-5y=-9%2C5x-6y=-8%29


5%283x-5y%29=5%28-9%29 Multiply the both sides of the first equation by 5.


15x-25y=-45 Distribute and multiply.


-3%285x-6y%29=-3%28-8%29 Multiply the both sides of the second equation by -3.


-15x%2B18y=24 Distribute and multiply.


So we have the new system of equations:
system%2815x-25y=-45%2C-15x%2B18y=24%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:


%2815x-25y%29%2B%28-15x%2B18y%29=%28-45%29%2B%2824%29


%2815x%2B-15x%29%2B%28-25y%2B18y%29=-45%2B24 Group like terms.


0x%2B-7y=-21 Combine like terms.


-7y=-21 Simplify.


y=%28-21%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=3 Reduce.


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15x-25y=-45 Now go back to the first equation.


15x-25%283%29=-45 Plug in y=3.


15x-75=-45 Multiply.


15x=-45%2B75 Add 75 to both sides.


15x=30 Combine like terms on the right side.


x=%2830%29%2F%2815%29 Divide both sides by 15 to isolate x.


x=2 Reduce.


So the solutions are x=2 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 3x-5y=-9 (red) and 5x-6y=-8 (green)