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

What does it mean when an inequality uses a solid line?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is either ≤ (less than or equal to) or ≥ (greater than or equal to).

Front

What does it mean when an inequality uses a dashed line?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is either < (less than) or > (greater than).

Front

How do you graph a system of inequalities?

Back

1. Graph each inequality on the same coordinate plane. 2. Use a solid line for ≤ or ≥ and a dashed line for < or >. 3. Shade the region that satisfies each inequality. 4. The solution is where the shaded regions overlap.

Front

What is the solution to the inequality y > 2x + 1?

Back

The solution is the region above the line y = 2x + 1, not including the line itself.

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 intersection of shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.

Front

What does the inequality y ≤ -3x + 4 represent graphically?

Back

It represents the region below the line y = -3x + 4, including the line itself.

Front

What is the graphical representation of the inequality y > -1?

Back

It represents the region above the horizontal line y = -1, not including the line.

Front

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

Back

The first step is to rewrite each inequality in slope-intercept form (y = mx + b) if necessary.