Systems of Equations: Graphing & 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 of solving a system of equations?

Back

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

Front

What is substitution in the context of 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 does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

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The system has no solution.

Front

What does it mean if two lines overlap?

Back

The system has infinitely many solutions.

Front

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

Back

If the equations represent parallel lines.

Front

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

Back

If the equations represent the same line.

Front

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

Back

Solve one of the equations for one variable.