Solving Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on a coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

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 does the solution to a system of linear inequalities look like?

Back

The solution to a system of linear inequalities is the region where the shaded areas of all inequalities overlap on the graph.

Front

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

Back

Substitute the coordinates 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 indicates the limit of the solutions; points on the line may or may not be included in the solution set, depending on the inequality.

Front

What does 'y < 2x + 2' represent graphically?

Back

It represents all the points below the line y = 2x + 2, not including the line itself.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered together.

Front

How do you solve a system of linear inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region as the solution.