at a concession stand, five hot dogs and two hamburgers cost $8.50, two hot dogs and five hamburger cost $10.75. find the cost of one hot dog and the cost of one hamburger.

5x+2y=8.5
2x+5y=10.75

you have the equations. Now just solve them.

To solve this system of linear equations, we can use either the substitution method or the elimination method. Let's use the elimination method to find the cost of one hot dog and one hamburger.

1. Multiply both sides of the first equation by 5 and the second equation by 2 to make the coefficients of 'y' equal:
Equation 1: 5*(5x + 2y) = 5*(8.5) -> 25x + 10y = 42.5
Equation 2: 2*(2x + 5y) = 2*(10.75) -> 4x + 10y = 21.5

2. Subtract the second equation from the first to eliminate 'y':
(25x + 10y) - (4x + 10y) = 42.5 - 21.5
25x - 4x + 10y - 10y = 21
21x = 21
x = 21/21
x = 1

Now we have the value of 'x', which represents the cost of one hot dog.

3. Substitute the value of x into either equation to find 'y':
Using the first equation, substitute x = 1:
5(1) + 2y = 8.5
5 + 2y = 8.5
2y = 8.5 - 5
2y = 3.5
y = 3.5/2
y = 1.75

Therefore, the cost of one hot dog is $1 and the cost of one hamburger is $1.75.