SOLUTION: Solve algebraically and check: 2x+4y=2 3x-6y=15

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Question 199100: Solve algebraically and check:
2x+4y=2
3x-6y=15
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%282x%2B4y=2%2C3x-6y=15%29


3%282x%2B4y%29=3%282%29 Multiply the both sides of the first equation by 3.


6x%2B12y=6 Distribute and multiply.


2%283x-6y%29=2%2815%29 Multiply the both sides of the second equation by 2.


6x-12y=30 Distribute and multiply.


So we have the new system of equations:
system%286x%2B12y=6%2C6x-12y=30%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:


%286x%2B12y%29%2B%286x-12y%29=%286%29%2B%2830%29


%286x%2B6x%29%2B%2812y%2B-12y%29=6%2B30 Group like terms.


12x%2B0y=36 Combine like terms.


12x=36 Simplify.


x=%2836%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=3 Reduce.


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6x%2B12y=6 Now go back to the first equation.


6%283%29%2B12y=6 Plug in x=3.


18%2B12y=6 Multiply.


12y=6-18 Subtract 18 from both sides.


12y=-12 Combine like terms on the right side.


y=%28-12%29%2F%2812%29 Divide both sides by 12 to isolate y.


y=-1 Reduce.


So the solutions are x=3 and y=-1.


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 2x%2B4y=2 (red) and 3x-6y=15 (green)



I'll let you do the check.