Systems - Graphing and Substitution

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are identical, meaning they lie on top of each other.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines when graphed.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.

Front

What is the graphical representation of parallel lines?

Back

Two lines that never meet, indicating no solution.

Front

What is the graphical representation of identical lines?

Back

Two lines that overlap completely, indicating infinitely many solutions.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable.