Solving Systems of Linear Inequalities — Quiz

Question 6 • Mathematics I

Which system of linear inequalities has the point 3 comma negative 2 in its solution set?

Answer

y is less than negative 3 y is greater than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line is parallel to the x-axis at y = negative 3. Everything below the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the left of this line is shaded.

y is greater than negative 3 y is greater than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 3. Everything above the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the left of this solid line is shaded.

y is less than negative 3 y is less than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 3. Everything below the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything below the line is shaded.

y is greater than negative 2 y is less than or equal to 2 thirds x minus 4 Image with description On a coordinate plane, 2 straight lines are shown. The scale on both axes ranges from negative 5 to 5 in increments of 1. The first dashed line is parallel to the x-axis at y = negative 2. Everything above the dashed line is shaded. The second solid line has a positive slope and goes through (0 comma negative 4) and (3 comma negative 2). Everything to the right of this solid line is shaded.

Explanation

Substitute x = 3 and y = −2 into choice B. The first inequality is −2 > −3, which is true. For the second, (2/3)(3) − 4 = −2, so −2 ≥ −2 is also true; therefore, the point satisfies both inequalities in choice B.

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