SOLUTION: using elimination method solve problem 3x-2y=-1 4x+y=6

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Question 191971: using elimination method solve problem 3x-2y=-1 4x+y=6
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-2y=-1%2C4x%2By=6%29


2%284x%2By%29=2%286%29 Multiply the both sides of the second equation by 2.


8x%2B2y=12 Distribute and multiply.


So we have the new system of equations:
system%283x-2y=-1%2C8x%2B2y=12%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:


%283x-2y%29%2B%288x%2B2y%29=%28-1%29%2B%2812%29


%283x%2B8x%29%2B%28-2y%2B2y%29=-1%2B12 Group like terms.


11x%2B0y=11 Combine like terms.


11x=11 Simplify.


x=%2811%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=1 Reduce.


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3x-2y=-1 Now go back to the first equation.


3%281%29-2y=-1 Plug in x=1.


3-2y=-1 Multiply.


-2y=-1-3 Subtract 3 from both sides.


-2y=-4 Combine like terms on the right side.


y=%28-4%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=2 Reduce.


So the solutions are x=1 and y=2.


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-2y=-1 (red) and 4x%2By=6 (green)