Answer these:

1. If two lines intersect, how many solutions exist?

2. If a system of two linear equations has no solution, what is true of their graphs?

3. Solve by substitution.

4

y x

y x

(2, 2)

one

Parallel Lines

More Substitution Method

Coordinate AlgebraStandard: A.REI.5

Essential Question

How do I solve a system of equations using the substitution method?

Substitution Method

Algebraic method used to solve a system of equations for an exact solution.

Use substitution property of equality to help you find the values of (x, y).

Remember, one equation in the system needs to be written as either x= or y= for this method.

Ex. 1)

Solve by substitution.

Answer: no solution

3 7

3 11

x y

y x

Ex. 2)

Solve by substitution.

Answer: Infinitely many solutions

7

3 3 21

x y

x y

Summarizer

Describe how to use substitution to solve the following system of linear equations.

5 1

2 3 7

y x

x y

T.O.t.D

How many solutions do the following systems have? Use the substitution method to help you decide.

2 41.

2 2

x y

x y

3 22.

12 4 8

x y

x y

NO Solution Infinite Solutions