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AssignmentMultiple Select

Solving Systems of Linear Inequalities

Question 8 • WV-Algebra I CR

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.

Answer
A
The slope of one boundary line is 2.
B
Both boundary lines are solid.
C
A solution to the system is (1, 3).
D
Both inequalities are shaded below the boundary lines.
E
The boundary lines intersect.

Explanation

The boundary lines are y = 3x + 1 and y = −x + 2, with slopes 3 and −1, so neither has slope 2. Because both inequalities include equality (≤ and ≥), both boundary lines are solid. The point (1, 3) satisfies both: 3 ≤ 3(1) + 1 and 3 ≥ −1 + 2. The first inequality is shaded below its line, but the second is shaded above, so D is false. The lines intersect because their slopes are different.

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