Let x = the unknown cost of a single hot dog and y = the unknown cost of a single soft drink. We have two unknowns so we need two equations to find them.
Equation 1 - 10 hot dogs and 5 soft drinks cost $35; that is 10x + 5y = 35
Equation 2 - 7 hot dogs and 4 soft drinks cost $25.25; that is 7x + 4y = 25.25
First let's re-write equation 1 to solve for y:
10x + 5y = 35
5y = 35 - 10x (subtract 10x from both sides)
y = 7 - 2x (divide both sides by 5)
Next, let's substitute 7 - 2x for y in equation 2:
7x + 4y = 25.25
7x + 4(7-2x) = 25.25
7x + 28 - 8x = 25.25
-x + 28 = 25.25
x - 28 = -25.25
Solve for x, the cost of a single hot dog. Once you have that, use y = 7 - 2x to find the cost of a single soft drink.