ISEE Word Problems Question 175: Answer and Explanation
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Question: 175
6. If x = 3t -5 and y = 7 -t, which of the following expresses y in terms of x?
- A. y =
- B. y =
- C. y = 7 -x
- D. y = 12 -3x
Correct Answer: B
Explanation:
The answer is B
Isolate t in the second equation by adding t to both sides and subtracting y from both sides: t = 7 - y. Now, substitute for t in the first equation: x = 3(7 - y) - 5. Distribute the 3: x = 21 - 3y - 5. Combine the 21 and -5: x = 16 - 3y. Add 3y to both sides and subtract x from both sides: 3y = 16 - x. Finally, divide both sides by 3: y = 
.
Plug in for t and solve for x and y. If t = 2, then 3(2) - 5 = 6 - 5 = 1 = x, and 7 - 2 = 5 = y. Plug in 1 for x in the expressions in the answer choices to find y = 5.