Question

Which ordered pair is a solution to this equation? 3x + 7y = 13

1) (2, 1)
2) (3, 1)
3) (4, 1)
4) (13, 2)

Answer 1

The ordered pair that is a solution to the equation 3x + 7y = 13 is (2, 1), as it is the only pair that, when plugged into the equation, yields a true statement.

Step-by-step explanation:

To determine which ordered pair is a solution to the equation 3x + 7y = 13, we need to plug in the x and y values from each ordered pair into the equation and check if the equation holds true. Let's test each option:

1. For the ordered pair (2, 1): 3(2) + 7(1) = 6 + 7 = 13 which is true, so (2, 1) is a solution.
2. For the ordered pair (3, 1): 3(3) + 7(1) = 9 + 7 = 16 which is not equal to 13, so (3, 1) is not a solution.
3. For the ordered pair (4, 1): 3(4) + 7(1) = 12 + 7 = 19 which is not equal to 13, so (4, 1) is not a solution.
4. For the ordered pair (13, 2): 3(13) + 7(2) = 39 + 14 = 53 which is not equal to 13, so (13, 2) is not a solution.

Therefore, the only ordered pair that satisfies the equation is (2, 1).