Question

Which ordered pair satisfies the equation 2x + 3y = 12?

a) (2,3)
b) (3,2)
c) (1,-2)
d) (-3,6)

Answer 1

The correct ordered pair that satisfies the equation 2x + 3y = 12 is (3,2). This is identified by substituting the x and y values from each option into the equation and verifying which pair equates to 12.

Step-by-step explanation:

To determine which ordered pair satisfies the equation 2x + 3y = 12, we can substitute the x and y values of each option into the equation and see which pair makes the equation true.

1. (2,3): Substitute x = 2 and y = 3 into the equation: 2(2) + 3(3) = 4 + 9 = 13. This does not equal 12, so it's not the correct pair.
2. (3,2): Substitute x = 3 and y = 2: 2(3) + 3(2) = 6 + 6 = 12. This equals 12, so this pair satisfies the equation.
3. (1,-2): Substitute x = 1 and y = -2: 2(1) + 3(-2) = 2 - 6 = -4. This does not equal 12, so it's not correct.
4. (-3,6): Substitute x = -3 and y = 6: 2(-3) + 3(6) = -6 + 18 = 12. Although this equals 12, it's not the correct pair because we already found a pair that satisfies the equation.

Therefore, the correct ordered pair that satisfies the equation 2x + 3y = 12 is (3,2).