Systems of Linear Equations and Inequalities

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

It means that the point satisfies all equations in the system.

Front

What are the three main methods to solve systems of equations?

Back

Graphing, Substitution, and Elimination.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines intersect at one point?

Back

It means there is exactly one solution to the system of equations.

Front

What is an inequality?

Back

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

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a solid line (if ≤ or ≥) or dashed line (if < or >) and shade the appropriate region.

Front

What is the solution set of a system of inequalities?

Back

The region on the graph where the shaded areas of all inequalities overlap.