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 with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. 3. Shade the region that satisfies the inequality.

Front

What does the solution of a system of linear inequalities represent?

Back

The solution represents all the points (x, y) that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Front

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

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

How can 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 a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. It divides the graph into two regions.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is '≥' or '≤', but not if it is '>' or '<'.

Front

How do you write a system of linear inequalities from a word problem?

Back

Identify the variables, translate the conditions into inequalities, and express them as a system.

Front

What is the graphical representation of the inequality y ≤ 2x + 1?

Back

The graph will have a solid line for y = 2x + 1 and the region below the line will be shaded.