Solving Systems by 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 substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Make sure at least one equation is solved for one variable.

Front

Back

(-5, -1)

Front

Back

(-3, 1)

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

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

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Back

(-2, -3)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.