Elimination and Substitution Method

At a concession stand, seven hot dogs and two hamburgers cost \$12.75; two hot dogs and seven hamburgers cost \$16.50. Find the cost of one hot dog and the cost of one hamburger.

Let x = cost of one hot dog

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y = cost of one hamburger Since there are two unknowns in this problem, we need two different equations to model the

problem. To find the first equation, we note that the cost of seven hot dogs and two hamburgers is

\$12.75. So we have… 7x + 2y = 12.75 To find the second equation, we note that the cost of the two hot dogs and seven hamburgers

is \$16.50. So we have…. 2x + 7y = 16.50 So, the system of equations we have is… 7x + 2y = 12.75

2x + 7y = 16.50 We can solve this system by using the “elimination” or the “substitution” method.

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