Systems of Linear Inequalities

Front

What does a solid line indicate in a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol has 'or equal to' (≤ or ≥).

Front

What is the solution set of the inequality y ≤ 3x?

Back

The solution set includes all points (x, y) where y is less than or equal to 3 times x.

Front

How do you represent a system of linear inequalities graphically?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

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 the point satisfies all inequalities, it is a solution.

Front

What does the overlap of shaded regions in a system of inequalities represent?

Back

The overlap represents the solution set for the system, where all inequalities are satisfied.

Front

What is the general form of a linear inequality in two variables?

Back

The general form is Ax + By < C, Ax + By ≤ C, Ax + By > C, or Ax + By ≥ C, where A, B, and C are constants.

Front

How do you write a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and ensure the equations represent the conditions given in the problem.

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 of a non-strict inequality (≤ or ≥), it is included in the solution set.

Front

What is the significance of the coefficients in a linear inequality?

Back

The coefficients determine the slope and direction of the boundary line in the graph of the inequality.