Inequalities and Systems of Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph the inequality y > -x - 1?

Back

To graph y > -x - 1, first graph the line y = -x - 1 as a dashed line, then shade the area above the line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert the equation 4x - y = 20 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = 4x - 20.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables.

Front

How do 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 it mean for a graph to represent a system of inequalities?

Back

It means that the graph shows the region where all the inequalities in the system are true.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system.