Systems of Equations 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 does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

Front

How do you solve a system of equations by substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of intersecting lines in a system of equations?

Back

It represents a system with one unique solution.

Front

What is the first step in solving a system of equations by graphing?

Back

Graph each equation on the same coordinate plane.

Front

If the equations in a system are identical, what is the solution?

Back

There are infinite solutions.

Front

What does it mean if two lines are skew?

Back

They do not intersect and are not parallel, existing in different planes.

Front

How can you verify if a point is a solution to a system of equations?

Back

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

Front

What is the substitution method?

Back

A method for solving systems of equations by expressing one variable in terms of the other.