Solving Systems by Substitution and Elimination

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 elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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, meaning every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

In the elimination method, what do you do if the coefficients of one variable are not the same?

Back

Multiply one or both equations by a number to make the coefficients the same.

Front

What is the purpose of rearranging equations in a system?

Back

To make it easier to apply the substitution or elimination methods.