Question

at a food truck festival, theres a challenge to guess the price of individual items in two different combo meals.

• combo a includes 1 burger and 2 fries and costs $11.
• combo b includes 2 burgers and 1 fry and costs $13.

the goal is to figure out the coat of a single burger (b) and one order of fries (f).
you can use this system of equations:

$$ \
LATEXBLOCK0
$$

question 1
what are the prices of one burger and one fries order?
burger = $5, fries = $3
burger = $4, fries = $3
burger = $6, fries = $2
burger = $3, fries = $4
question 2
what does it mean that one pair of values works in both combos?
its the solution to the system
it only works in the second combo
it shows there are infinite combos
the items cost the same

Explanation:

Step1: Solve the system of equations

We have the system \(

$$\begin{cases}b + 2f=11\\2b + f = 13\end{cases}$$

\).
From the first equation \(b=11 - 2f\).
Substitute \(b = 11-2f\) into the second equation:
\(2(11 - 2f)+f=13\).
Expand: \(22-4f + f=13\).
Combine like - terms: \(22-3f=13\).
Subtract 22 from both sides: \(-3f=13 - 22=-9\).
Divide both sides by \(-3\): \(f = 3\).

Step2: Find the value of \(b\)

Substitute \(f = 3\) into \(b=11 - 2f\).
\(b=11-2\times3=11 - 6 = 5\).

Answer:

Question 1: Burger = $5, Fries = $3
Question 2: It's the solution to the system