Solving Systems of Linear Inequalities — Quiz

Question 9 • Mathematics 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 On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The fist solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (negative 3 comma 2). Everything to the left of the solid line is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (negative 1 comma negative 2). Everything to the left of the solid is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. The second solid line goes through the points (negative 2 comma 0) and (0 comma 4). Everything to the right of the solid line is shaded.

Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 3 to 7 in increments of 1. There are two solid lines on the graph. The first solid line goes through the points (0 comma 1) and (5 comma 0). Everything above the solid line is shaded. A second solid line goes through the points (2 comma 0) and (0 comma 4). Everything to the left of the solid line is shaded.

Explanation

Rewrite the first inequality, x + 5y ≥ 5, as y ≥ 1 − x/5. Its solid boundary passes through (0, 1) and (5, 0), with shading above it. The second inequality is y ≤ 2x + 4, whose solid boundary passes through (−2, 0) and (0, 4); the solution is below this rising line, which is the region to its right. Choice C shows both boundaries and shading correctly.

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz