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.
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