Solving System of Equations that have 0, 1, and Infinite Solutions

1
Solving System of Equations that have 0, 1, and
Infinite Solutions
2
One Solution

• Solve the following system of equation
  algebraically and graphically

The lines only intersect once since there is one
solution.
Both equations equal y. Set them equal to each
other.
3
No Solution

• Solve the following system of equation
  algebraically and graphically

The two lines are parallel. They never intersect.
Add the equations to eliminate a variable
No Solution.
4
Infinite Solutions

• Solve the following system of equation
  algebraically and graphically

The two equations are equivalent. They lie on
top of each other. They intersect everywhere.
True
Infinite Solutions. Every point that satisfies
THE LINES COINCIDE