Solving 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 one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you solve a system of equations using substitution?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical representation of a system of equations?

Back

The solutions are represented by the points where the graphs of the equations intersect.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(−2, −1)

Front

What is the solution to the system of equations y = 4x - 5 and y = 2x + 1?

Back

(3, 7)

Front

What does it mean if two equations are dependent?

Back

They represent the same line, leading to infinitely many solutions.