Solving Systems of Linear Inequalities — Quiz

Question 8 • Mathematics I

Which graph shows the solution to the system of linear inequalities? x plus 3 y is greater than 6 y is greater than or equal to 2 x plus 4

Answer

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma negative 2) and (3 comma negative 1). Everything below the dashed line is shaded. The second line is a solid line that goes through the points (2 comma 0) and (4 comma 4). Everything to the left of the solid line is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma negative 2) and (3 comma negative 1). Everything below the dashed line is shaded. The second line is a solid line that goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma 2) and (3 comma 1). Everything above the dashed line is shaded. The second line is a solid line that goes through the points (2 comma 0) and (4 comma 4). Everything to the left of the solid line is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two straight lines on the graph. The first line is a dashed line that goes through the points (0 comma 2) and (3 comma 1). Everything above the dashed line is shaded. The second line is a solid line that goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.

Explanation

Rewrite the first inequality as y > −(1/3)x + 2. Its boundary is dashed because the inequality is strict, and the solution is above the line through (0, 2) and (3, 1). The second inequality is y ≥ 2x + 4, so its boundary is solid and the solution lies above that line, which is the region to its left. Choice D shows both boundaries and shaded regions correctly.

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