Many, None, One Solutions

x + 6 = x

• one

• none

• infinite

2x + 4 = - (-7x + 6)

• one

• none

• infinite

5n - 1 = 5n + 4

• one

• none

• infinite

6n - 1 = n + 3

• one

• none

• infinite

6x + 9 – x = 3x + 9 + x

• No Solution

• One Solution

• Infinite Solutions

How many solutions would this system of equations have?

• No solution

• One Solution

• Infinite Solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 8 = 3(x - 4) + 1

• one

• no solutions

• infinite solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 7 = 3(x - 3) + 2

• one

• no solutions

• infinite solutions

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 no 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