No, One, and Infinite Many Solutions

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
5x + 6 = 2 + 3x

• one

• no solutions

• infinite solutions

14 - 2 ( 3p + 1) = 6 ( 4 + p)

• No Solution

• One Solution

• Infinite Solutions

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

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

• No Solution

• One Solution

• Infinite Solutions

How many solutions does the following equation have? −2x + 9 + 6x = −3x + 2

• One Solution

• No Solutions

• Infinitely Many Solutions

• Two solutions

How many solutions does the following equation have?

−5x + 5 − 4x = −1 − 9x

• One Solution

• No Solutions

• Infinitely Many Solutions

• Two solutions

Based on the equations for each line, determine how many solutions the system would have.

y=2x+3

y=-4x+3

• Infinite Number of Solutions

• No Solution

• One Solution

Based on the equations for each line, determine how many solutions the system would have.

y=-3x+2

y=-3x+2

• Infinite Number of Solutions

• No Solution

• One Solution

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

Based on the equations for each line, determine how many solutions the system would have.

y=5x+3

y=5x-2

• Infinite Number of Solutions

• No Solution

• One Solution