Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

Front

What does the inequality y ≤ x - 3 represent?

Back

It represents all points (x, y) on or below the line y = x - 3.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary line.

Front

What does the solution to the inequality y < -2 look like on a graph?

Back

It is represented by a horizontal line at y = -2, with a dashed line indicating that points on the line are not included, and shading below the line.

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 significance of the boundary line in an inequality?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. The line itself may or may not be included in the solution, depending on whether the inequality is strict or inclusive.

Front

What does the inequality y ≥ -x + 1 represent?

Back

It represents all points (x, y) on or above the line y = -x + 1.

Front

How can you tell if an inequality is graphed correctly?

Back

Check if the shaded region corresponds to the inequality sign and if the boundary line is solid (for ≥ or ≤) or dashed (for > or <).

Front

What is the solution set of the inequalities y > -4/5x - 1 and y ≤ 2/3x + 3?

Back

The solution set is the region where the area above the line y = -4/5x - 1 and below the line y = 2/3x + 3 overlap.