Modeling with Systems of Linear Inequalities — Quiz
Question 6 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY
A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y , and the number of open acres, x , can be no more than 1 Which graph represents the system of inequalities for this scenario? x plus y is greater than or equal to 4 y minus x is less than or equal to 1
Answer
A
Image with description On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 1 comma 0) and (0 comma 1). Everything above and to the left of the line is shaded. The second line has a negative slope and goes through (0 comma 4) and (4 comma 0). Everything to the left of the line is shaded.
B
Image with description On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4 comma 0) and (0 comma 4). Everything to the left of the line is shaded. The second line has a negative slope and goes through (0 comma 1) and (1 comma 0). Everything to the left of the line is shaded.
C
Image with description On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 1 comma 0) and (0 comma 1). Everything below and to the right of the line is shaded. The second line has a negative slope and goes through (0 comma 4) and (4 comma 0). Everything above and to the right of the line is shaded.
D
Image with description On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4 comma 0) and (0 comma 4). Everything to the right of the line is shaded. The second line has a negative slope and goes through (0 comma 1) and (1 comma 0). Everything to the right of the line is shaded.
Explanation
The condition x + y ≥ 4 becomes y ≥ −x + 4, so its solid boundary passes through (0, 4) and (4, 0), with the region above the line shaded. The condition y − x ≤ 1 becomes y ≤ x + 1, whose solid boundary passes through (−1, 0) and (0, 1), with the region below the line shaded. Choice C shows both boundaries and the correct shaded sides.
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