Solving Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities that involve the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does it mean if a point is a solution to a system of linear inequalities?

Back

A point is a solution to a system of linear inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

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

What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be greater than or equal to the number on the right side of the inequality.

Front

What is the solution set of the inequality y > 2?

Back

The solution set of the inequality y > 2 includes all points above the horizontal line y = 2, not including the line itself.

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. The type of line (solid or dashed) indicates whether points on the line are included in the solution.

Front

What does the graph of 'y < -x + 3' look like?

Back

The graph of 'y < -x + 3' has a dashed line for the equation y = -x + 3, and the region below the line is shaded.

Front

What is the solution to the system of inequalities: y ≤ 2x - 1 and y > -2x + 3?

Back

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