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At an airport restaurant, 2 sodas and 4 hamburgers cost $12.00. An order of 4 sodas and 2 hamburgers costs $9.00. How much does one hamburger cost?

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TVD2468
Let's say the sodas are each $1. If you have purchased 4 sodas it will cost $4. You still have $5 left on your bill. If you have 2 hamburgers left on your bill the amount of each hamburger is $2.50.
Let the cost of soda be s.
Let the cost of hamburgers = h

[tex]\begin{cases} &2s + 4h = 12 ----- (1) \\&4s + 2h = 9 ----- (2)\end{cases}[/tex]

Multiply Equation (1) by 2 :
[tex]\begin{cases} &4s + 8h = 24 ----- (1)\\&4s + 2h = 9 ----- (2)\end{cases}[/tex]

Equation (1) - (2):
[tex]\begin{aligned} &6h = 15 \\&h = 2.5 \end{aligned} [/tex]

Answer: 1 hamburger costs $2.50