Number of Solutions to Linear Equations

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

4(x - 5) + 3 = 2(2x + 9)

• one solution

• no solution

• infinitely many 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 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 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

• one solution

• no solution

• infinite solutions

3(x-2) + 1 = 3x - 5

• No Solution

• One Solution

• Infinite Solutions

Solve:
2x + 1 = 2x - 1

• No Solution

• x = 0

• Infinitely Many 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