SOLUTION: x+2y=10, 3x+4y=8

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Question 189588: x+2y=10,
3x+4y=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%28x%2B2y=10%2C3x%2B4y=8%29


-3%28x%2B2y%29=-3%2810%29 Multiply the both sides of the first equation by -3.


-3x-6y=-30 Distribute and multiply.


So we have the new system of equations:
system%28-3x-6y=-30%2C3x%2B4y=8%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:


%28-3x-6y%29%2B%283x%2B4y%29=%28-30%29%2B%288%29


%28-3x%2B3x%29%2B%28-6y%2B4y%29=-30%2B8 Group like terms.


0x%2B-2y=-22 Combine like terms.


-2y=-22 Simplify.


y=%28-22%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=11 Reduce.


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-3x-6y=-30 Now go back to the first equation.


-3x-6%2811%29=-30 Plug in y=11.


-3x-66=-30 Multiply.


-3x=-30%2B66 Add 66 to both sides.


-3x=36 Combine like terms on the right side.


x=%2836%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=-12 Reduce.


So the solutions are x=-12 and y=11.


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 x%2B2y=10 (red) and 3x%2B4y=8 (green)