Solving Systems of Linear Inequalities — Quiz

Question 7 • Mathematics I

Which graph shows the solution to the system of linear inequalities? y is less than or equal to 2 x minus 5 y is greater than negative 3 x plus 1

Answer

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0 comma 1) and (1comma negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the right of the line is shaded.

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 1) and (1 comma negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the right of the line is shaded.

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0 comma 1) and (1 comma negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the left of the line is shaded.

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 1) and (1 comma negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0 comma negative 5) and (2 comma negative 1). Everything to the left of the line is shaded.

Explanation

The boundary for y ≤ 2x − 5 is solid because equality is included; its line has positive slope and y-intercept −5. The boundary for y > −3x + 1 is dashed because equality is excluded; its line has negative slope and y-intercept 1. The solution regions are on the right side of both lines, matching choice B.

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