One, No, and Infinitely Many Solutions

Solve:
2x + 1 = 2x - 1

• No Solution

• x = 0

• Infinitely Many Solutions

Solve:
3x + 15 = 3(x + 5)

• No Solution

• x = 15

• Infinitely Many Solutions

5x + 4 = 5x − 3

• x = 4

• x = -3

• infinitely many solutions

• no solutions

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

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

What is the solution to the system of linear equations graphed below?

• No Solution

• Infinitely Many Solutions

• One Solution: (0 , 4)

• One Solution: (0, -6)

How many solutions does the system of equations below have?

• One Solution

• No Solution

• Infinitely Many Solutions Infinitely Many Solutions

How many solutions does the system of equations below have?

• One Solution

• No Solution

• Infinitely Many Solutions Infinitely Many Solutions

What is the solution to the system of linear equations graphed below?

• No Solution

• Infinitely Many Solutions

• One Solution: (1, -2)

• One Solution: (-2, 1)

What is the solution to the system of linear equations graphed below?

• No Solution

• Infinitely Many Solutions

• One Solution: (4, 2)

• One Solution: (2, 4)