SOLUTION: HEEEEELLLPPPP please.....solve by the elimination method....... x + 4y = 21 and -x + 3y = 0.......type an ordered pair

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Question 550485: HEEEEELLLPPPP please.....solve by the elimination method....... x + 4y = 21 and -x + 3y = 0.......type an ordered pair
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%2B4y=21%2C-x%2B3y=0%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2B4y%29%2B%28-1x%2B3y%29=%2821%29%2B%280%29


%281x%2B-1x%29%2B%284y%2B3y%29=21%2B0 Group like terms.


0x%2B7y=21 Combine like terms.


7y=21 Simplify.


y=%2821%29%2F%287%29 Divide both sides by 7 to isolate y.


y=3 Reduce.


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x%2B4y=21 Now go back to the first equation.


x%2B4%283%29=21 Plug in y=3.


x%2B12=21 Multiply.


x=21-12 Subtract 12 from both sides.


x=9 Combine like terms on the right side.


So the solutions are x=9 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 x%2B4y=21 (red) and -x%2B3y=0 (green)