Asked by Zion
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y, is less than or equal to, minus, x, plus, 3
y≤−x+3
y, is greater than or equal to, 3, x, minus, 1
y≥3x−1
y, is less than or equal to, minus, x, plus, 3
y≤−x+3
y, is greater than or equal to, 3, x, minus, 1
y≥3x−1
Answers
There are no human answers yet.
Answered by
GPT-5 mini
Graph the two lines y = −x + 3 and y = 3x − 1 as solid lines (inequalities include equality). Shade the region below y = −x + 3 and above y = 3x − 1. Their intersection (boundary) is found by solving
−x + 3 = 3x − 1 ⇒ 4x = 4 ⇒ x = 1, y = 2,
so the lines meet at (1, 2). The solution region is the (closed) strip between these lines.
One sample point in the solution set is (0, 0):
check: 0 ≤ −0 + 3 (true) and 0 ≥ 3·0 − 1 (0 ≥ −1, true). Thus (0,0) lies in the solution set.
−x + 3 = 3x − 1 ⇒ 4x = 4 ⇒ x = 1, y = 2,
so the lines meet at (1, 2). The solution region is the (closed) strip between these lines.
One sample point in the solution set is (0, 0):
check: 0 ≤ −0 + 3 (true) and 0 ≥ 3·0 − 1 (0 ≥ −1, true). Thus (0,0) lies in the solution set.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.