Graphing System of Linear Inequalities

Front

What does the inequality y ≥ x - 3 represent on a graph?

Back

The area above the line y = x - 3 is shaded, indicating all points where y is greater than or equal to x - 3.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the first step in solving a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane.

Front

What does the inequality y < -x - 1 indicate about the graph?

Back

The area below the line y = -x - 1 is shaded, indicating all points where y is less than -x - 1.

Front

Which of the following points is a solution to the inequality y ≥ x + 4? (0, 5), (1, 3), (2, 6)

Back

(0, 5) is a solution because 5 ≥ 0 + 4 is true.

Front

What is the solution set of the system of inequalities y ≥ -x - 1 and y < x + 4?

Back

The solution set is the region where the area above the line y = -x - 1 and below the line y = x + 4 overlap.

Front

How do you graph the inequality y > -x - 1?

Back

Graph the line y = -x - 1 as a dashed line and shade above it.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If the inequality is ≤ or ≥, the point is included in the solution set; if it is < or >, the point is not included.

Front

What is the significance of the shaded region in a graph of linear inequalities?

Back

The shaded region represents all possible solutions that satisfy the inequalities.

Front

How can you check if a point is NOT part of the solution set?

Back

Substitute the point into the inequalities; if it does not satisfy at least one inequality, it is not part of the solution set.