SOLUTION: The difference between two numbers is 9. The sum of twice the larger number and three times the smaller number is 33. Find the two numbers. i came up with this... x-y=9 2x+3

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The difference between two numbers is 9. The sum of twice the larger number and three times the smaller number is 33. Find the two numbers. i came up with this... x-y=9 2x+3      Log On


   

Question 228088: The difference between two numbers is 9. The sum of twice the larger number and three times the smaller number is 33. Find the two numbers.

i came up with this...
x-y=9
2x+3y=33
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-y=9%2C2x%2B3y=33%29


3%28x-y%29=3%289%29 Multiply the both sides of the first equation by 3.


3x-3y=27 Distribute and multiply.


So we have the new system of equations:
system%283x-3y=27%2C2x%2B3y=33%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-3y%29%2B%282x%2B3y%29=%2827%29%2B%2833%29


%283x%2B2x%29%2B%28-3y%2B3y%29=27%2B33 Group like terms.


5x%2B0y=60 Combine like terms.


5x=60 Simplify.


x=%2860%29%2F%285%29 Divide both sides by 5 to isolate x.


x=12 Reduce.


------------------------------------------------------------------


3x-3y=27 Now go back to the first equation.


3%2812%29-3y=27 Plug in x=12.


36-3y=27 Multiply.


-3y=27-36 Subtract 36 from both sides.


-3y=-9 Combine like terms on the right side.


y=%28-9%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=3 Reduce.


So the solutions are x=12 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-y=9 (red) and 2x%2B3y=33 (green)