Final answer:
Each of the given ordered pairs a) (5, 31), b) (-6, -24), c) (0, 6), and d) (2, 16) correctly satisfies the equation y = 5x + 6. They can all be considered correct solutions to the equation, demonstrating how to find solutions to linear equations.
Step-by-step explanation:
Finding Ordered Pairs in a Linear Equation
To determine which ordered pairs satisfy the equation y = 5x + 6, we need to plug in the x-values from each ordered pair into the equation and see if the resulting y-value matches the one in the ordered pair.
- For the ordered pair (5, 31), plugging in x = 5 gives us y = 5(5) + 6 = 25 + 6 = 31, which matches the y-value in the pair.
- For the ordered pair (-6, -24), plugging in x = -6 gives us y = 5(-6) + 6 = -30 + 6 = -24, which matches the y-value in the pair.
- For the ordered pair (0, 6), plugging in x = 0 gives us y = 5(0) + 6 = 0 + 6 = 6, which matches the y-value in the pair.
- For the ordered pair (2, 16), plugging in x = 2 gives us y = 5(2) + 6 = 10 + 6 = 16, which also matches the y-value in the pair.
All the given ordered pairs a) (5, 31), b) (-6, -24), c) (0, 6), and d) (2, 16) satisfy the equation y = 5x + 6. Therefore, each of these is a correct option. However, as per the question's request to mention the correct option in the final answer, we need to specify one. If the question requires only one correct pair, it should be clarified as all the options listed are correct.