SOLUTION: find the coordinates of -x+3y=12, and 4x+3y=12

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Question 243643: find the coordinates of -x+3y=12, and 4x+3y=12
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%28-x%2B3y=12%2C4x%2B3y=12%29


4%28-x%2B3y%29=4%2812%29 Multiply the both sides of the first equation by 4.


-4x%2B12y=48 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2B12y=48%2C4x%2B3y=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:


%28-4x%2B12y%29%2B%284x%2B3y%29=%2848%29%2B%2812%29


%28-4x%2B4x%29%2B%2812y%2B3y%29=48%2B12 Group like terms.


0x%2B15y=60 Combine like terms.


15y=60 Simplify.


y=%2860%29%2F%2815%29 Divide both sides by 15 to isolate y.


y=4 Reduce.


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-4x%2B12y=48 Now go back to the first equation.


-4x%2B12%284%29=48 Plug in y=4.


-4x%2B48=48 Multiply.


-4x=48-48 Subtract 48 from both sides.


-4x=0 Combine like terms on the right side.


x=%280%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=0 Reduce.


So the solutions are x=0 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 -x%2B3y=12 (red) and 4x%2B3y=12 (green)