Question

Explain which method you used for solving the system of equations in which x represents the number of bottles of water sold and y represents the number of sandwiches sold.

x + y = 390 and 2x + 4y = 1260

Answer 1

To solve the system of equations:

1. **Identify the system of equations:**
- Equation 1: \( x + y = 390 \)
- Equation 2: \( 2x + 4y = 1260 \)

2. **Choose a method:**
In this case, I will use the **substitution method** to solve the system. I could also use the elimination method, but substitution is straightforward given that Equation 1 can be easily manipulated to express one variable in terms of another.

3. **Solve for one variable:**
From Equation 1, we can express \( y \) in terms of \( x \):
\[
y = 390 - x
\]

4. **Substitute into the other equation:**
Next, we substitute \( y \) from Equation 1 into Equation 2:
\[
2x + 4(390 - x) = 1260
\]
Simplifying this gives:
\[
2x + 1560 - 4x = 1260
\]
\[
-2x + 1560 = 1260
\]

5. **Isolate \( x \):**
Now, we can isolate \( x \):
\[
-2x = 1260 - 1560
\]
\[
-2x = -300
\]
Dividing both sides by -2:
\[
x = 150
\]

6. **Substitute back to find \( y \):**
Now that we have \( x = 150 \), we can substitute back to find \( y \):
\[
y = 390 - x = 390 - 150 = 240
\]

7. **Conclusion:**
The solution to the system of equations is:
\[
x = 150 \quad \text{(bottles of water sold)}
\]
\[
y = 240 \quad \text{(sandwiches sold)}
\]

This method provided a clear way to isolate variables and substitute, leading to the solution of the problem efficiently.