SOLUTION: 3x+5y=0 x+4y=-7

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Question 151479: 3x+5y=0
x+4y=-7
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%2B5y=0%2Cx%2B4y=-7%29


-3%28x%2B4y%29=-3%28-7%29 Multiply the both sides of the second equation by -3.


-3x-12y=21 Distribute and multiply.


So we have the new system of equations:
system%283x%2B5y=0%2C-3x-12y=21%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%2B5y%29%2B%28-3x-12y%29=%280%29%2B%2821%29


%283x%2B-3x%29%2B%285y%2B-12y%29=0%2B21 Group like terms.


0x%2B-7y=21 Combine like terms. Notice how the x terms cancel out.


-7y=21 Simplify.


y=%2821%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=-3 Reduce.


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3x%2B5y=0 Now go back to the first equation.


3x%2B5%28-3%29=0 Plug in y=-3.


3x-15=0 Multiply.


3x=0%2B15 Add 15 to both sides.


3x=15 Combine like terms on the right side.


x=%2815%29%2F%283%29 Divide both sides by 3 to isolate x.


x=5 Reduce.


So our answer is x=5 and y=-3.


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%2B5y=0 (red) and x%2B4y=-7 (green)