Systems of Equations and Inequalities Review

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 are the three main methods for solving systems of equations?

Back

Graphing, Substitution, and Elimination.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What does the graph of intersecting lines represent?

Back

A unique solution to the system of equations, where the lines cross at one point.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the coordinates of the point into both equations; if both equations are true, the point is a solution.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

What is the Fundamental Theorem of Arithmetic?

Back

It is not a method for solving systems of equations; it states that every integer greater than 1 can be expressed uniquely as a product of prime numbers.