Final answer:
The three ordered-pair solutions of the equation 2x + 3y = 6 are (0, 2), (3, 0), and (1, 1).
Step-by-step explanation:
The equation 2x + 3y = 6 is a linear equation in two variables. To find the ordered-pair solutions, we can substitute values for x and solve for y. Let's check the given options:
- (a) (0, 2): When x = 0, 2(0) + 3y = 6, which simplifies to 3y = 6 and y = 2. So, (0, 2) is a solution.
- (b) (1, 2): When x = 1, 2(1) + 3y = 6, which simplifies to 2 + 3y = 6 and 3y = 4. Solving for y, we get y = 4/3. So, (1, 2) is not a solution.
- (c) (2, 1): When x = 2, 2(2) + 3y = 6, which simplifies to 4 + 3y = 6 and 3y = 2. Solving for y, we get y = 2/3. So, (2, 1) is not a solution.
- (d) (3, 0): When x = 3, 2(3) + 3y = 6, which simplifies to 6 + 3y = 6 and 3y = 0. Solving for y, we get y = 0. So, (3, 0) is a solution.
Therefore, the three ordered-pair solutions of the equation 2x + 3y = 6 are (0, 2), (3, 0), and (1, 1). Hence, the correct option is (a) (0, 2), (3, 0), (1, 1).