To solve this system of equations:
1) Multiply the first equation by 2 to make the coefficients of y the same in both equations:
6x + 12y = 96
2) Subtract the second equation from the modified first equation to eliminate y:
6x + 12y - (6x + 4y) = 96 - 60
8y = 36
y = $4.50
3) Substitute the value of y back into the first equation to solve for x:
3x + 4(4.50) = 48
3x + 18 = 48
3x = 30
x = $10
Therefore, a burger meal costs $10 and a hot dog meal costs $4.50.