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

What does the symbol '>' represent in a graph?

Back

The symbol '>' indicates that the boundary line is not included in the solution set, meaning points on the line are not solutions.

Front

What does the symbol '≥' indicate in a graph?

Back

The symbol '≥' indicates that the boundary line is included in the solution set, meaning points on the line are solutions.

Front

How do you determine which side of the boundary line to shade for the inequality y < 2x + 3?

Back

To determine which side to shade, pick a test point not on the line (like (0,0)). If the point satisfies the inequality, shade that side; otherwise, shade the opposite side.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you graph the inequality y ≥ 3?

Back

Graph a horizontal line at y = 3, use a solid line, and shade above the line.

Front

What is the solution to the system of inequalities y < x + 2 and y > -x + 1?

Back

The solution is the region where the shaded areas of both inequalities overlap.

Front

How can you check 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 does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is a solution only if the inequality includes equality (≥ or ≤).

Front

What is the graphical representation of the inequality x + y < 4?

Back

Graph the line x + y = 4 with a dashed line and shade below the line.