https://file.aiquickdraw.com/mathbot/file/17253681929077zm1e1ef.jpg

The image you uploaded contains a mathematical question. Let me extract the problem and solve it for you.

---

**Problem Statement:**
The equation given is:

\[
3x + 2y = 12
\]

You are asked to identify which one of the following points is a solution to this equation:
- (2, 3)
- (4, 0)
- (0, 6)
- (-2, 9)

**Solution:**

To determine which point is a solution, substitute the values of \(x\) and \(y\) from each point into the equation \(3x + 2y = 12\) and check if the equation holds true.

1. **Point (2, 3):**
   \[
   3(2) + 2(3) = 6 + 6 = 12 \quad \text{(True)}
   \]
   This point satisfies the equation.

2. **Point (4, 0):**
   \[
   3(4) + 2(0) = 12 + 0 = 12 \quad \text{(True)}
   \]
   This point also satisfies the equation.

3. **Point (0, 6):**
   \[
   3(0) + 2(6) = 0 + 12 = 12 \quad \text{(True)}
   \]
   This point also satisfies the equation.

4. **Point (-2, 9):**
   \[
   3(-2) + 2(9) = -6 + 18 = 12 \quad \text{(True)}
   \]
   This point also satisfies the equation.

**Conclusion:**

All the given points (2, 3), (4, 0), (0, 6), and (-2, 9) satisfy the equation \(3x + 2y = 12\). Therefore, **all of these points** are solutions to the equation.

---

Would you like a more detailed explanation or have any further questions?

Here are some related questions you might find helpful:

1. How do you solve systems of linear equations using substitution or elimination?
2. What is the graphical representation of a linear equation in two variables?
3. How can you find the intercepts of a linear equation?
4. What are the methods to determine if a point lies on a given line?
5. How can you check solutions for non-linear equations?

**Tip:** When solving for the solution to an equation, always substitute the values back into the original equation to ensure they satisfy it.

Which of the following points is a solution to the equation 3x + 2y = 12?
- (2, 3)
- (4, 0)
- (0, 6)
- (-2, 9)

Learn how to determine which points satisfy the linear equation 3x + 2y = 12. This problem covers algebraic concepts related to linear equations and coordinate geometry, ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation