Solving Systems of Linear Inequalities — Quiz

Question 5 • Mathematics I

Which graph shows the solution to the system of linear inequalities? x minus 4 y is less than or equal to 4 y is less than x plus 1

Answer

Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything to the left of the solid line is shaded. The second dashed line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything to the right of the dashed line is shaded.

Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything to the left of the solid line is shaded. The second solid line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything to the right of the dashed line is shaded.

Image with description On a coordinate plane, 2 straight lines are shown. The scale on the x and y axes ranges from negative 5 to 5. The first solid line has a positive slope and goes through the points (0 comma negative 1) and (4 comma 0). Everything below the solid line is shaded. The second dashed line also has a positive slope and goes through the points (negative 1 comma 0) and (0 comma 1). Everything below the dashed line is shaded.

Explanation

Rearrange x − 4y ≤ 4 to get y ≥ x/4 − 1. Its boundary is the solid line through (0, −1) and (4, 0), and the solution is above that line, described as the region to its left. The other inequality, y < x + 1, uses a dashed boundary through (−1, 0) and (0, 1), with the solution below it, or to its right. Choice A shows both boundaries and shaded regions correctly.

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