Linear Inequalities and Systems of Equations

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 (>, <, ≥, ≤).

Front

What does the solution of a linear inequality represent?

Back

The solution of a linear inequality represents all the values that satisfy the inequality, often visualized as a range of numbers on a number line.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when substituted into the inequality.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

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

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system of equations has an infinite number of solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

To determine if a point is a solution to a system of inequalities, substitute the point into each inequality. If it satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality x < -1?

Back

The graphical representation of x < -1 is a dashed vertical line at x = -1, with the region to the left shaded.