SOLUTION: solve the following system of equations x and y 18x+6y=120 4x+3y=40

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Question 257305: solve the following system of equations x and y
18x+6y=120
4x+3y=40
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%2818x%2B6y=120%2C4x%2B3y=40%29


-2%284x%2B3y%29=-2%2840%29 Multiply the both sides of the second equation by -2.


-8x-6y=-80 Distribute and multiply.


So we have the new system of equations:
system%2818x%2B6y=120%2C-8x-6y=-80%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:


%2818x%2B6y%29%2B%28-8x-6y%29=%28120%29%2B%28-80%29


%2818x%2B-8x%29%2B%286y%2B-6y%29=120%2B-80 Group like terms.


10x%2B0y=40 Combine like terms.


10x=40 Simplify.


x=%2840%29%2F%2810%29 Divide both sides by 10 to isolate x.


x=4 Reduce.


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18x%2B6y=120 Now go back to the first equation.


18%284%29%2B6y=120 Plug in x=4.


72%2B6y=120 Multiply.


6y=120-72 Subtract 72 from both sides.


6y=48 Combine like terms on the right side.


y=%2848%29%2F%286%29 Divide both sides by 6 to isolate y.


y=8 Reduce.


So the solutions are x=4 and y=8.


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 18x%2B6y=120 (red) and 4x%2B3y=40 (green)