Introduction to Systems of Linear Equations

Solving Systems of Equations with Graphing

One Solution

• The two lines intersect (touch) at ONE POINT

• Your answer should be an ordered pair (x, y)

• What is its location?

Multiple Choice

What is the solution?

• (1, -1)
• (-1, 1)
• (0, -2)
• (0, 1)

No Solution

• The two lines NEVER intersect (touch)

• The lines are PARALLEL

Multiple Choice

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

Infinitely Many Solution

• The equations are on SAME LINE

• You have infinitely many solutions.

Multiple Choice

How many solutions will this system have? (Hint: There is a pink line and a blue line, one on top of the other.)

• one solution

• no solution

• infinitely many solutions

Different types of solutions

1. One solution: The solution is where the points intersect

2. No solution: The lines will never intersect so this system does not have an answer

3. Infinite solutions: The lines have the same equation.

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

Which system of linear equations has no solution?

Multiple Choice

What is the solution to the following system of equations?

• (-3, 1)

• (1, 3)

• Infinitely Many Solutions

• No Solution

Multiple Choice

How many solutions will this system have?

• one solution

• no solution

• infinitely many solutions