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Question 3 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

A salad is made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3 Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4 Which graph represents the system of equations for this scenario?

Answer
A
Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0 comma 4) and (2 comma 3). Everything below the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 3) and (2 comma 1). Everything to the right of the line is shaded.
B
Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0 comma negative 3) and (2 comma 1). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0 comma 2) and (4 comma 0). Everything below of the line is shaded.
C
Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0 comma 4) and (2 comma 3). Everything below the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 3) and (2 comma 1). Everything to the left of the line is shaded.
D
Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0 comma negative 3) and (2 comma 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0 comma 2) and (4 comma 0). Everything below of the line is shaded.

Explanation

Let g be the ounces of greens and c the ounces of carrots. The first condition is 2g − c ≥ 3, or c ≤ 2g − 3, so its boundary is the solid line through (0, −3) and (2, 1), with the region below it (to its right) shaded. The second condition is g + 2c < 4, or c < 2 − g/2, so its boundary is the dashed line through (0, 2) and (4, 0), with the region below shaded. Choice B shows both inequalities.

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