SOLVING SYSTEMS OF EQUATIONS

USING SUBSTITUTION

Textbook Section 6-2

WARM-UP Which inequality does not have the

same solution as ?

LEARNING TARGET Students can solve a system of

equations using substitution. Students can classify systems as

consistent, inconsistent, dependent, or independent using algebraic methods.

QUICK DISCUSSION What does the word substitute mean? Provide examples.

In sports, coaches often substitute one player for another who plays the same position.

In school, when a teacher is absent, a substitute teacher takes his/her place for the day.

STEPS FOR SOLVING A SYSTEM OF LINEAR EQUATIONS USING SUBSTITUTION

1) Solve for either variable, if necessary. 2) Substitute the resulting expression into

the other equation. 3) Solve that equation to get the value of

the first variable. 4) Substitute that value into one of the

original equations and solve for the second variable.

5) Write the values from steps 3 and 4 as an ordered pair (x, y). Check your answer.

Solve the following systems using substitution. State the number of

solutions (no solution, one solution, or infinite solutions) and tell whether the

system is consistent, inconsistent, dependent, or independent.

EXAMPLE 1 Solve the system using substitution.

One Solution (5, 10)Consistent Independent

EXAMPLE 2 Solve the system using substitution.

One Solution (3, -1)Consistent Independent

EXAMPLE 3 Solve the system using substitution.

Infinite Solutions Consistent Dependent

EXAMPLE 4Solve the system using substitution.

No Solution Inconsistent

THINGS TO REMEMBER… When solving the system, if the end

result is a false (for example, 2 = -5), the answer is no solution.

If the end result is a statement that is always true (for example, 3 = 3, or x = x), the system has infinite solutions.

If you can solve for the variables, there is one solution (for example, x = 3, y = 1).