https://file.aiquickdraw.com/mathbot/file/1727350628737ueri2ynj.jpg

The equation given in the image is \( 2x = 7y = 28 \), which can be interpreted as two separate equations:

\[
2x = 28 \quad \text{and} \quad 7y = 28
\]

1. Solve \( 2x = 28 \):
   \[
   x = \frac{28}{2} = 14
   \]

2. Solve \( 7y = 28 \):
   \[
   y = \frac{28}{7} = 4
   \]

Thus, the solution to the system of equations is \( x = 14 \) and \( y = 4 \). Now, we check which of the given options is **not** a solution:

### Option (a) \( (7, 2) \):
- For \( x = 7 \):
  \[
  2x = 2(7) = 14 \quad (\text{not } 28)
  \]
Thus, option (a) is **not** a solution.

### Checking the other options:

### Option (b) \( (0, 4) \):
- For \( x = 0 \):
  \[
  2x = 2(0) = 0 \quad (\text{not } 28)
  \]
So, (b) is **also not** a solution.

### Option (c) \( (2, 7) \):
- For \( x = 2 \):
  \[
  2x = 2(2) = 4 \quad (\text{not } 28)
  \]
Thus, (c) is **not** a solution.

### Option (d) \( (14, 0) \):
- For \( x = 14 \):
  \[
  2x = 2(14) = 28
  \]
- For \( y = 0 \):
  \[
  7y = 7(0) = 0 \quad (\text{not } 28)
  \]
Thus, (d) is **also not** a solution.

However, **(a)** is the first incorrect one when compared directly to the expected solutions.

Let me know if you want to dive deeper into the explanation or solve further problems.

### Follow-up questions:
1. How would you graph the equation \( 2x + 7y = 28 \)?
2. How do you test for solutions in a system of linear equations?
3. Can you generalize this method for a different equation?
4. What are the key steps to solving linear equations in two variables?
5. How would this method change if the equation involved fractions?

### Tip:
When solving systems of equations, always check each possible solution by substituting the values of both variables to ensure correctness.

Which option is not a solution of 2x = 7y = 28? Options: (a) (7, 2), (b) (0, 4), (c) (2, 7), (d) (14, 0)

Explore how to identify which ordered pairs do not solve the linear equation system 2x = 7y = 28. We evaluate options such as (7, 2), (0, 4), (2, 7), and (14, 0) through substitution. Suitable for Grades 6-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation