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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

What is a system of inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality.

Front

What does the solution of a system of inequalities represent?

Back

The region where the shaded areas of all inequalities overlap.

Front

What is substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is elimination in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where all equations are satisfied.