Question

Help me please!! Joe went to a fast food restaurant and bought 4 orders of fries and 2 burgers for $14. Becca went to the same fast food restaurant and bought 3 orders of fries and one burger for $9.
Question:

Write a system of equations that models this situation. Let x represent orders of fries and y represent burgers.

Answer 1

Here are the equations that are represented by the scenarios:

4x + 2y = $14 (Joe)
3x + y = $9 (Becca) or y = 9 - 3x

To find the cost of each burger and fry you will solve the second equation for y and substitute it in for the y in the first equation.  This will put everything in terms of x, the price of a fry.

4x + 2(9 - 3x) = $14
4x + 18 - 6x = 14
-2x +18 = 14
     -18     -18
    -2x = -4
    -2      -2
     x = 2

Fry cost $2, and burgers cost (9 - 3 x 2) or $3.