Solving Systems by 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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the graphical method for solving systems of equations?

Back

Plotting each equation on a graph and identifying the point(s) where they intersect.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression derived from another equation.

Front

How do you determine if a system has one solution?

Back

If the lines representing the equations intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

Back

(1, 3)

Front

Back

(2, 1)

Front

Back

(-2, -3)