SOLUTION: x+9y=48 -x+6y=27

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Question 214741: x+9y=48
-x+6y=27
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%2B9y=48%2C-x%2B6y=27%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%2B9y%29%2B%28-x%2B6y%29=%2848%29%2B%2827%29


%28x-x%29%2B%289y%2B6y%29=48%2B27 Group like terms.


0x%2B15y=75 Combine like terms.


15y=75 Simplify.


y=%2875%29%2F%2815%29 Divide both sides by 15 to isolate y.


y=5 Reduce.


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x%2B9y=48 Now go back to the first equation.


x%2B9%285%29=48 Plug in y=5.


x%2B45=48 Multiply.


x=48-45 Subtract 45 from both sides.


x=3 Combine like terms on the right side.


So the solutions are x=3 and y=5.


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%2B9y=48 (red) and -x%2B6y=27 (green)