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 for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

It means the lines coincide, or are the same line.

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

How do you graph a linear equation?

Back

By finding at least two points that satisfy the equation and connecting them with a straight line.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

How can you determine if a system of equations has no solution graphically?

Back

If the lines are parallel and do not intersect.

Front

How can you determine if a system of equations has infinitely many solutions graphically?

Back

If the lines overlap completely.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable.