Question

E. Use your graph to help you list three viable solutions to the problem when 2.00x + 1. 00y = 30.

Answer 1

F. Suppose Santiago bought 26 books. Can you figure out how many of each type of book he bought? Explain. Write a system of equations and solve algebraically. Use Demos Calculator to check your work by adding the equation x + y = 26 to the graph above to help you answer the question.

Answer 2

Make is shorter please

Answer 3

To find viable solutions for the equation \(2.00x + 1.00y = 30\), we can solve for \(y\) in terms of \(x\):

\[
1.00y = 30 - 2.00x
\]
\[
y = 30 - 2x
\]

To identify three viable solutions, we can choose different values for \(x\) and compute the corresponding \(y\) values.

1. **Choose \(x = 0\)**:
\[
y = 30 - 2(0) = 30
\]
Solution: \((0, 30)\)

2. **Choose \(x = 10\)**:
\[
y = 30 - 2(10) = 30 - 20 = 10
\]
Solution: \((10, 10)\)

3. **Choose \(x = 15\)**:
\[
y = 30 - 2(15) = 30 - 30 = 0
\]
Solution: \((15, 0)\)

Thus, three viable solutions to the equation \(2.00x + 1.00y = 30\) are:
1. \((0, 30)\)
2. \((10, 10)\)
3. \((15, 0)\)

Answer 4

Let's define two variables to represent the number of each type of book Santiago bought:

- Let \( x \) be the number of the first type of book.
- Let \( y \) be the number of the second type of book.

From the information given, we can create the following system of equations:

1. The total number of books equation:
\[
x + y = 26
\]

2. The equation that comes from the problem statement you provided earlier \(2.00x + 1.00y = 30\), which can also represent the prices or some other condition regarding the books.

So the system of equations is:
\[
\begin{align*}
1. & \quad x + y = 26 \quad \text{(1)} \\
2. & \quad 2x + y = 30 \quad \text{(2)}
\end{align*}
\]

Now, we will solve this system of equations algebraically.

### Step 1: Solve Equation (1) for \(y\)

From equation (1):
\[
y = 26 - x \quad \text{(3)}
\]

### Step 2: Substitute Equation (3) into Equation (2)

Substituting (3) into equation (2):
\[
2x + (26 - x) = 30
\]

### Step 3: Simplify and solve for \(x\)

\[
2x + 26 - x = 30
\]
\[
x + 26 = 30
\]
\[
x = 30 - 26
\]
\[
x = 4
\]

### Step 4: Substitute \(x\) back into Equation (3) to find \(y\)

Now, substitute \(x = 4\) back into equation (3):
\[
y = 26 - 4 = 22
\]

### Conclusion

Santiago bought:
- \(x = 4\) books of the first type,
- \(y = 22\) books of the second type.

### Check the Results

Now, let's verify this solution with the second equation:
\[
2(4) + 22 = 8 + 22 = 30
\]
The second equation is satisfied.

### Use the Calculator to Graph

You can graph the two equations:
1. \(x + y = 26\)
2. \(2x + y = 30\)

The intersection point of these two lines represents the solution to the system, which in this case should be \((4, 22)\).

### Final Answer

Santiago bought **4 books of the first type** and **22 books of the second type**.

Answer 5

Sure! Here's a concise solution:

### Definition of Variables
- Let \( x \) = number of the first type of book
- Let \( y \) = number of the second type of book

### System of Equations
1. \( x + y = 26 \) (total books)
2. \( 2x + y = 30 \) (price condition)

### Solve the System
1. From equation 1:
\[
y = 26 - x
\]

2. Substitute into equation 2:
\[
2x + (26 - x) = 30
\]
\[
2x + 26 - x = 30
\]
\[
x + 26 = 30 \quad \Rightarrow \quad x = 4
\]

3. Find \( y \):
\[
y = 26 - 4 = 22
\]

### Conclusion
Santiago bought:
- **4 books of the first type**
- **22 books of the second type**

This solution satisfies both equations!