System of Equations and Inequalities

Front

What is a system of equations?

Back

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

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

An ordered pair is a solution if it satisfies all equations in the system.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.

Front

What is the graphical representation of a linear inequality?

Back

A region of the coordinate plane that shows all the solutions to the inequality.

Front

How do you determine if an ordered pair is a solution to an inequality?

Back

Substitute the ordered pair into the inequality and check if the statement is true.

Front

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

Back

'>' means greater than, while '≥' means greater than or equal to.

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 can you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping region.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.