Question

Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points)
Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points)
Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)

Answer 1

I don't have the original two equations from your problem. Could you paste them here? Once I have them I’ll solve and explain.

Meanwhile, here’s what I’ll do for Steps 2–4 and why:

Step 2 — Method chosen
- I choose the elimination (addition/subtraction) method.
- Why: elimination is usually quickest and least error-prone for a 2×2 linear system because you can directly remove one variable by scaling and adding/subtracting the equations; it avoids fractions until necessary and is easy to follow.

Step 3 — How to solve (general template using elimination)
Suppose your system is
a·m + b·n = c
d·m + e·n = f

1. Multiply the first equation by a constant so that the coefficient of one variable matches (in magnitude) the corresponding coefficient in the second equation. For example, to eliminate m, multiply the first equation by d and the second by a so both have coefficient a·d on m:
(d a)·m + (d b)·n = d c
(a d)·m + (a e)·n = a f

2. Subtract the two equations to eliminate m:
(d b − a e)·n = d c − a f

3. Solve for n:
n = (d c − a f) / (d b − a e)

4. Substitute that n back into one of the original equations and solve for m:
m = (c − b·n) / a (assuming a ≠ 0)

(Equivalently you can eliminate n first and solve for m; or use the formula for a 2×2 system:
m = (c e − b f) / (a e − b d),
n = (a f − c d) / (a e − b d).)

Step 4 — Meaning of the solutions
- m = (number you find) is the cost per night (or whichever variable m represents), in dollars (or the currency used).
- n = (number you find) is the cost per meal (or whichever variable n represents), in dollars.
Each value tells how much one unit (one night or one meal) costs based on the combined totals used to form the system.

If you paste the specific equations, I’ll carry out these steps with the actual numbers and give the numeric answers and units.