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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.