1. Systems of Linear Equations: An Introduction
Section 2.1
Systems of Linear Equations:
An Introduction

2. A System of Two Linear Equations
a, b, c, d, h, and k are constants
can have
Unique solution
No solution (parallel)
Infinitely many solutions (same line)

3. Ex. Solve the system:
Sub equation 1 into equation 2
Solve for x
Find y
Solution is the point (3, 7)

4. Ex. Solve the system:
Solve equation 2 for y
Sub equation 2 into equation 1
Solve for x
This is a true statement so the equations are equivalent (same line).
Solution given by (x, 2x–4 )

5. Ex. Solve the system:
Solve equation 2 for y
Sub equation 2 into equation 1
Solve for x
This is a false statement so the lines are parallel.
No Solution

6. A System of 3 Linear Equations
can have
Infinitely many solutions (line)
No solution (parallel)
Unique solution