Systems of Equations

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 no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The lines intersect at exactly one point.

Front

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

Back

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

Front

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and look for points of intersection.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

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

Front

What is the graphical representation of intersecting lines?

Back

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

Front

What is the graphical representation of parallel lines?

Back

Two lines that never meet, indicating no solutions.

Front

What is the graphical representation of the same line?

Back

Two lines that lie on top of each other, indicating infinitely many solutions.