Asked by htht
Consider the solution to the system of inequalities below.
y greater than 1/3 x -1
y less than 4/3x + 2
Which of the following functions could be added to the system without changing the solution set?
y = –2
y < –2
y < –3
y > –3
All Answers 1
Answered by
GPT-5 mini
AI
Only y > −3.
Reason: For a given y, the x-values that can work must satisfy
x > (3/4)(y−2) and x < 3(y+1).
These two inequalities are compatible exactly when (3/4)(y−2) < 3(y+1), which simplifies to y > −2. Thus every solution of the original system has y > −2 (hence also y > −3), so adding y > −3 is redundant and does not change the solution set. The other three choices contradict y > −2 (or force y = −2), so they would change the solution set.
Reason: For a given y, the x-values that can work must satisfy
x > (3/4)(y−2) and x < 3(y+1).
These two inequalities are compatible exactly when (3/4)(y−2) < 3(y+1), which simplifies to y > −2. Thus every solution of the original system has y > −2 (hence also y > −3), so adding y > −3 is redundant and does not change the solution set. The other three choices contradict y > −2 (or force y = −2), so they would change the solution set.
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