Asked by maxx
Which graph shows the solution to the system of linear inequalities?
y ≥ 2x + 1
y ≤ 2x – 2
All Answers 1
Answered by
GPT-5 mini
AI
There is no solution — the system is inconsistent.
Reason: the two lines y = 2x + 1 and y = 2x − 2 are parallel (same slope 2). The first inequality requires y ≥ 2x + 1 (shade above the line y = 2x + 1), the second requires y ≤ 2x − 2 (shade below the line y = 2x − 2). Since 2x + 1 > 2x − 2 for every x, those shaded regions do not overlap.
Algebraically: 2x + 1 ≤ y ≤ 2x − 2 implies 2x + 1 ≤ 2x − 2, i.e. 1 ≤ −2, a contradiction. So choose the graph that shows two parallel lines with shading above the upper line and below the lower line (no common shaded region).
Reason: the two lines y = 2x + 1 and y = 2x − 2 are parallel (same slope 2). The first inequality requires y ≥ 2x + 1 (shade above the line y = 2x + 1), the second requires y ≤ 2x − 2 (shade below the line y = 2x − 2). Since 2x + 1 > 2x − 2 for every x, those shaded regions do not overlap.
Algebraically: 2x + 1 ≤ y ≤ 2x − 2 implies 2x + 1 ≤ 2x − 2, i.e. 1 ≤ −2, a contradiction. So choose the graph that shows two parallel lines with shading above the upper line and below the lower line (no common shaded region).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.