SOLUTION: 3x - 6y = -3 and 2x + 4y = 30

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Question 282618: 3x - 6y = -3 and 2x + 4y = 30
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-6y=-3%2C2x%2B4y=30%29


2%283x-6y%29=2%28-3%29 Multiply the both sides of the first equation by 2.


6x-12y=-6 Distribute and multiply.


3%282x%2B4y%29=3%2830%29 Multiply the both sides of the second equation by 3.


6x%2B12y=90 Distribute and multiply.


So we have the new system of equations:
system%286x-12y=-6%2C6x%2B12y=90%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-12y%29%2B%286x%2B12y%29=%28-6%29%2B%2890%29


%286x%2B6x%29%2B%28-12y%2B12y%29=-6%2B90 Group like terms.


12x%2B0y=84 Combine like terms.


12x=84 Simplify.


x=%2884%29%2F%2812%29 Divide both sides by 12 to isolate x.


x=7 Reduce.


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6x-12y=-6 Now go back to the first equation.


6%287%29-12y=-6 Plug in x=7.


42-12y=-6 Multiply.


-12y=-6-42 Subtract 42 from both sides.


-12y=-48 Combine like terms on the right side.


y=%28-48%29%2F%28-12%29 Divide both sides by -12 to isolate y.


y=4 Reduce.


So the solutions are x=7 and y=4.


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-6y=-3 (red) and 2x%2B4y=30 (green)