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Question 7 • Algebra I

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

Answer

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two solid lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line passes through 0 comma 1 and negative 2 comma negative 3. The red line passes through 0 comma negative 2 and 1 comma 0. The region above the blue line is shaded blue, the region below the red line is shaded orange, and the region between the two lines is not shaded.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line is solid and passes through 0 comma 1 and negative 2 comma negative 3. The red line is dashed and passes through 0 comma negative 2 and 1 comma 0. The region above the blue line is shaded blue, the region below the red line is shaded orange, and the region between the two lines is not shaded.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two solid lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line passes through 0 comma 1 and negative 2 comma negative 3. The red line passes through 0 comma negative 2 and 1 comma 0. The region to the left of the blue line is shaded orange, the region between the two lines is shaded purple, and the region to the right of the red line is shaded blue.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis sits on a grid in increments of 1. The horizontal x-axis is labeled from negative 5 to 5. The vertical y-axis is labeled from negative 7 to 3. Two lines with arrowheads on both ends have a positive slope and run parallel to each other. The blue line is solid and passes through 0 comma 1 and negative 2 comma negative 3. The red line is dashed and passes through 0 comma negative 2 and 1 comma 0. The region to the left of the blue line is shaded orange, the region between the two lines is shaded purple, and the region to the right of the red line is shaded blue.

Explanation

Both boundary lines have slope 2: y = 2x + 1 and y = 2x − 2. Since the inequalities include equality, both lines should be solid. The solution would need to be above or on y = 2x + 1 and below or on y = 2x − 2, but the first line is always 3 units above the second, so those shaded regions never overlap. Choice B shows the solid boundaries and the two non-overlapping shaded regions.

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