lesson pretestMultiple Choice

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Question 2 • Algebra I

Which graph shows the solution to the system of linear inequalities? x plus 5 y is greater than or equal to 5 y is less than or equal to 2 x plus 4

Answer

Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points, negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points, negative 5 comma 5, negative 2 comma 0 and negative 1 comma negative 2, with the region to the left of the line shaded. The two lines intersect between 2 and 3 on the x-axis and 1 and 2 on the y-axis. The region where both shades collide in the second quadrant is highlighted in a different shade.

Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points negative 1 comma 6, 0 comma 4, and 2 comma 0, with the region to the left of the line shaded. The two lines intersect between 1 and 2 on the x-axis and 0 and 1 on the y-axis. The region where both shades collide in the first and second quadrants is highlighted in a different shade.

Image with description A coordinate plane with the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1, featuring 2 solid lines with shaded regions. The first solid line passes through the points negative 4 comma 2, 0 comma 1, and 4 comma 0, with the region above the line shaded. The second solid line passes through the points negative 3 comma negative 2, negative 2 comma 0 and 0 comma 4, with the region to the right of the line shaded. The two lines intersect between negative 1 and negative 2 on the x-axis and 1 and 2 on the y-axis. The region where both shades collide in the first and second quadrants is highlighted in a different shade.

Explanation

The boundary for y ≤ 2x + 4 is the solid line y = 2x + 4, which passes through (−2, 0) and (0, 4). The solution is below this line, on its right-hand side in the graph, so the second line and shading match choice B. The first inequality also requires shading above its boundary, as shown there.

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