One, None or Infinite Solutions

8z - 22 = 3 ( 3z + 11) -z

• No Solution

• One Solution

• Infinite Solutions

12 (x + 3 ) = 4 (2x + 9 ) +4x

• No Solution

• One Solution

• Infinite Solutions

6x + 9 – x = 3x + 9 + x

• No Solution

• One Solution

• Infinite Solutions

6x - 18 = 4(2x - 3) - (2x + 6)

• No Solution

• One Solution

• Infinite Solution

What is the definition of one solution?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

• only this ONE solution will make the equation true

What is the definition of infinite solutions?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

• only this ONE solution will make the equation true

You solved out a system of equations and got:

4 = 3.

What does this mean about the system?

• One solution (you can find x and y)

• No solution (parallel lines)

• Infinite solutions (same line)

You solved out a system of equations and got:

5 = 5.

What does this mean about the system?

• One solution (you can find x and y)

• No solution (parallel lines)

• Infinite solutions (same line)

You solved out a system of equations and got:

x = 5.

What does this mean about the system?

• One solution (you can find x and y)

• No solution (parallel lines)

• Infinite solutions (same line)

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions