Solving systems of linear inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities involving the same variables.

Front

What does it mean if a system of linear inequalities has no solution?

Back

It means that there is no set of values for the variables that satisfies all inequalities in the system.

Front

What does it mean if a system of linear inequalities has an infinite number of solutions?

Back

It means that there are countless combinations of values for the variables that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

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

Back

The boundary line divides the coordinate plane into two half-planes, one of which contains the solutions to the inequality.

Front

When do you flip the inequality sign?

Back

When you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution set of a system of linear inequalities?

Back

The set of all points (x, y) that satisfy all inequalities in the system.

Front

What does the graph of y > 2 look like?

Back

A dashed horizontal line at y = 2, with the area above the line shaded.

Front

What does the graph of y ≤ 2 look like?

Back

A solid horizontal line at y = 2, with the area below the line shaded.

Front

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

Back

Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it is a solution.