Solve 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 ordered pairs that satisfy all inequalities in the system.

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line. The line is solid if the inequality is inclusive (≥ or ≤) and dashed if it is exclusive (> or <).

Front

What is the difference between 'y > mx + b' and 'y ≥ mx + b'?

Back

'y > mx + b' represents a dashed line and does not include points on the line, while 'y ≥ mx + b' represents a solid line and includes points on the line.

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 appropriate half-plane for each inequality. 4. The solution is where the shaded regions overlap.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all ordered pairs that satisfy all inequalities.

Front

What does it mean for a point to be outside the solution set of a system of inequalities?

Back

A point is outside the solution set if it does not satisfy at least one of the inequalities in the system, meaning it lies in a region that is not shaded.

Front

How can you check if an ordered pair is a solution to a system of inequalities?

Back

Substitute the x and y values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. It helps determine the solution set.