Question

Which of the following is true about the solution to the system of inequalities shown? y≤1/3x-1 y≤1/3x-3

1) The solution is a single point
2) The solution is a line
3) The solution is a shaded region
4) The solution is empty

Answer 1

The solution to the system of inequalities y≤1/3x-1 and y≤1/3x-3 is a shaded region below both lines on a graph.

Step-by-step explanation:

The given system of inequalities is y≤1/3x-1 and y≤1/3x-3. When graphing these inequalities, each will form a line with a slope of 1/3, but with different y-intercepts. Since both inequalities are y≤ (less than or equal to), the region that would be the solution for these inequalities is the area that lies below both lines.

If we graph these lines, we will find that the area below both lines is a shaded region. Therefore, the solution to the system of inequalities is not a single point, a line, or empty, but rather a shaded region where the conditions of both inequalities are true.