Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

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 one side of a boundary line.

Front

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

Back

To determine if a point is a solution, substitute the point's coordinates into the inequality. If the inequality holds true, the point is a solution.

Front

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

Back

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

Front

What does the symbol 'y < 3' represent on a graph?

Back

The symbol 'y < 3' represents all points below the horizontal line y = 3, not including the line itself.

Front

What is the solution set of the inequality 'y > 2x - 4'?

Back

The solution set includes all points above the line y = 2x - 4, excluding the line itself.

Front

How can you graph the system of inequalities 'y < 2' and 'y > 2x - 4'?

Back

Graph the line y = 2 as a dashed line (not included) and shade below it. Then graph y = 2x - 4 as a dashed line and shade above it. The solution is where the shaded regions overlap.

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 a solution only if the inequality is non-strict (≤ or ≥). If the inequality is strict (< or >), the point is not a solution.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.