Solving Systems of Equations Using Substitution

Objective: Solve systems of linear equations using substitution

The Substitution Method

1. Solve one of the equations for a variable (preferably choose a variable with a coefficient of 1)

2. Substitute the expression found in the first step in the other equation of the system.

3. Solve the resulting equation for the second variable.

4. Substitute the value obtained for the second variable into one of the original equations.

5. Solve for the remaining variable.

Example:

x - 2 y = 8

2 x + y = 8

Solve the first equation for x:	x = 2 y + 8
Substitute in the second equation:	2(2 y + 8) + y = 8
Solve:	4 y + 16 + y = 8 5 y = -8
Substitute into the first equation:
Solve		is the solution
Check your work using 2nd Equation:	8 = 8

There are 3 possibilities for Solving Systems using Substitution:

1. A value for both variables will be determined.

One solution exists, and the system is consistent and equations are independent

2. The substitution will result in a contradiction.

No solution exists and the system is inconsistent and equations are independent.

3. The substitution will result in an identity.

An infinite number of solutions exist and the system is consistent and equations are dependent.