SOLUTION: 4x-6y=3 6x-4y=-3 solve by elimination method

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Question 366974: 4x-6y=3
6x-4y=-3
solve by elimination method
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%284x-6y=3%2C6x-4y=-3%29


4%284x-6y%29=4%283%29 Multiply the both sides of the first equation by 4.


16x-24y=12 Distribute and multiply.


-6%286x-4y%29=-6%28-3%29 Multiply the both sides of the second equation by -6.


-36x%2B24y=18 Distribute and multiply.


So we have the new system of equations:
system%2816x-24y=12%2C-36x%2B24y=18%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:


%2816x-24y%29%2B%28-36x%2B24y%29=%2812%29%2B%2818%29


%2816x%2B-36x%29%2B%28-24y%2B24y%29=12%2B18 Group like terms.


-20x%2B0y=30 Combine like terms.


-20x=30 Simplify.


x=%2830%29%2F%28-20%29 Divide both sides by -20 to isolate x.


x=-3%2F2 Reduce.


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16x-24y=12 Now go back to the first equation.


16%28-3%2F2%29-24y=12 Plug in x=-3%2F2.


-24-24y=12 Multiply.


-24y=12%2B24 Add 24 to both sides.


-24y=36 Combine like terms on the right side.


y=%2836%29%2F%28-24%29 Divide both sides by -24 to isolate y.


y=-3%2F2 Reduce.


So the solutions are x=-3%2F2 and y=-3%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.


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

Also, feel free to check out my tutoring website

Jim