At a concession stand, three hotdogs and two hamburgers cost 8.50, two hotdogs and three hamburgers cost 9.00. What is the cost of one hamburger and one hotdog?

So far I have:
x=hotdog
y-hamburger
3x+2y=8.50
2x+3y=9.00
For the life of me I cannot remember any of the steps past that. Any help would be awesome.

Question

At a concession stand, three hotdogs and two hamburgers cost 8.50, two hotdogs and three hamburgers cost 9.00. What is the cost of one hamburger and one hotdog?

So far I have:
x=hotdog
y-hamburger
3x+2y=8.50
2x+3y=9.00
For the life of me I cannot remember any of the steps past that. Any help would be awesome.

jim_thompson5910 · Answer

Let's say we want to eliminate the y term. So we want the y coefficients to be equal but opposite in sign. This way, when we add the equations, they add to 0 and go away.

jim_thompson5910 · Answer

To do this, multiply every term in the first equation by 3 to get


3x+2y=8.50

3(3x)+3(2y)=3(8.50)

9x+6y = 25.5

jim_thompson5910 · Answer

Then multiply every term in the second equation by -2


2x+3y=9.00

-2*(2x)+(-2)*(3y)=-2*(9.00)

-4x-6y = -18

jim_thompson5910 · Answer

So we now have the equations 


9x+6y = 25.5
-4x-6y = -18

Add them to get 


9x+6y = 25.5
-4x-6y = -18
-------------
5x+0y = 7.5


Which gives you 5x = 7.5

anonymous · Answer

Thank you so much. As soon as you started explaining it it call came flooding back! Much appreciated!

jim_thompson5910 · Answer

that's great, glad it helped