Final answer:
The correct ordered pair that satisfies both systems of equations 2s/3t = 1 and 3t = 2s is (3, 2), which is option (a). The solution is found by expressing s in terms of t and verifying which pair satisfies both equations.
Step-by-step explanation:
To solve the given system of equations 2s/3t = 1 and 3t = 2s, we can first solve for one variable in terms of the other using the second equation and then substitute into the first. From the second equation, we can express s as s = (3/2)t. Substituting this into the first equation gives 2((3/2)t)/(3t) = 1, which simplifies to 1 = 1. This shows that the second equation depends on the first, and we can use either equation to find the relationship between s and t. Since 3t = 2s, we see that (s, t) = (3, 2) satisfies the equation, making it the correct ordered pair.
Checking the answer choices:
- (a) (3, 2): 2(3)/3(2) = 1 and 3(2) = 2(3) are both true.
- (b) (-2, -3): 2(-2)/3(-3) != 1 and 3(-3) != 2(-2) do not satisfy both equations.
- (c) (1, 3): 2(1)/3(3) != 1 and 3(3) != 2(1) do not satisfy both equations.
- (d) (0, 0): Cannot compute 2s/3t as t = 0 leads to division by zero, and 3t != 2s when both are zero.
Therefore, the correct final answer is option (a) which is the ordered pair (3, 2).