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 is the solution of a system of equations?

Back

The ordered pair that satisfies all equations in the system.

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

How do you graph a system of equations?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is the substitution method 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 the elimination method 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 does it mean for two lines to be intersecting?

Back

They cross at exactly one point, which is the solution to the system of equations.

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 graphical representation of a system of equations with no solution?

Back

Two parallel lines that never meet.