SOLUTION: solve the system of equations: 6x-y=3 5x+3y=-9

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Question 347764: solve the system of equations:
6x-y=3
5x+3y=-9
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%286x-y=3%2C5x%2B3y=-9%29


3%286x-y%29=3%283%29 Multiply the both sides of the first equation by 3.


18x-3y=9 Distribute and multiply.


So we have the new system of equations:
system%2818x-3y=9%2C5x%2B3y=-9%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:


%2818x-3y%29%2B%285x%2B3y%29=%289%29%2B%28-9%29


%2818x%2B5x%29%2B%28-3y%2B3y%29=9%2B-9 Group like terms.


23x%2B0y=0 Combine like terms.


23x=0 Simplify.


x=%280%29%2F%2823%29 Divide both sides by 23 to isolate x.


x=0 Reduce.


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


18x-3y=9 Now go back to the first equation.


18%280%29-3y=9 Plug in x=0.


0-3y=9 Multiply.


-3y=9-0 Subtract 0 from both sides.


-3y=9 Combine like terms on the right side.


y=%289%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=-3 Reduce.


So the solutions are x=0 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 6x-y=3 (red) and 5x%2B3y=-9 (green)


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

Also, feel free to check out my tutoring website

Jim