Systems of Inequalities Test

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

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, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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 the coordinates of the point are substituted into the inequality.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane, which is the region of the graph that satisfies the inequality. The boundary line is dashed for 'greater than' or 'less than' and solid for 'greater than or equal to' or 'less than or equal to'.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What is the difference between '<' and '≤' in inequalities?

Back

'< ' means that the value is strictly less than, while '≤' means that the value is less than or equal to.

Front

How do you graph the inequality y > -2x + 1?

Back

To graph y > -2x + 1, first graph the line y = -2x + 1 as a dashed line. Then shade the region above the line, as it represents all points where y is greater than -2x + 1.

Front

How do you graph the inequality y ≤ x + 3?

Back

To graph y ≤ x + 3, first graph the line y = x + 3 as a solid line. Then shade the region below the line, as it represents all points where y is less than or equal to x + 3.

Front

What is the solution region for a system of inequalities?

Back

The solution region for a system of inequalities is the area where the shaded regions of all inequalities overlap. This region contains all the points that satisfy all inequalities in the system.

Front

What does it mean to solve a system of inequalities by graphing?

Back

Solving a system of inequalities by graphing involves graphing each inequality on the same coordinate plane and identifying the overlapping region that represents the solution.