You now have two equations with the same two unknowns, $p$ and $k$. How can you combine these equations (for example, by subtracting) to eliminate one variable?

After you eliminate $p$, solve for $k$. Then plug that value of $k$ back into either original equation to solve for $p$, the fixed fee.

In a Desmos expression line, type k = (26 - 13.5) / (8 - 3) and look at the value Desmos gives for $k$. This is the cost per mile.

On a new line, type p = 13.5 - k * 3. The value Desmos shows for $p$ is the fixed pickup fee in dollars.

Use the model $C = p + km$.

• For the $3$-mile delivery that costs $13.50:
  • $13.50 = p + 3k$
• For the $8$-mile delivery that costs $26.00:
  • $26 = p + 8k$

Now you have a system of two equations in the two unknowns $p$ and $k$.

Subtract the first equation from the second to eliminate $p$:

So

The cost per mile is $2.5$ dollars per mile (but the question is asking for $p$).

Use $k = 2.5$ in one of the original equations, for example $13.50 = p + 3k$:

Subtract $7.5$ from both sides:

So the fixed pickup fee $p$ is $6$ dollars.