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To solve this system of linear equations, we first need to rewrite the second equation in terms of s:
7h - 55 = 15
7h = 70
h = 10
Now that we have the value for h, we can substitute it back into the first equation to solve for s:
4h + 4s = 10
4(10) + 4s = 10
40 + 4s = 10
4s = -30
s = -7.5
Therefore, the cost of a hot dog is $10 and the cost of a soda is -$7.50 (or $7.50 given the context of the problem).