### 15-2: Solutions – One, None, or Infinitely Many

#### Key Concept

One Solution A linear equation in one variable has one solution if only one value of the variable makes the equation true.

In this situation, you transform the original equation into simpler equivalent equations until the variable is alone on one side of the equal sign, and a number is alone on the other. For example: No Solution A linear equation in one variable has no solution if no value of the variable makes the two sides of the equation equal.

You know that an equation has no solution when, as you solve for the variable, you get a false statement. For example: The equation has no solution.

Infinitely Many Solutions A linear equation in one variable has infinitely many solutions if any value of the variable makes the two sides of the equation equal.

You know that an equation has infinitely many solutions when, as you solve for the variable, you get a true statement. For example: The equation has infinitely many solutions.

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