One Solution, No Solution, Infinitely Many Solutions

Front

What does it mean if an equation has 'One Solution'?

Back

An equation has 'One Solution' if there is exactly one value of the variable that satisfies the equation.

Front

What does it mean if an equation has 'No Solution'?

Back

An equation has 'No Solution' if there are no values of the variable that can satisfy the equation.

Front

What does it mean if an equation has 'Infinitely Many Solutions'?

Back

An equation has 'Infinitely Many Solutions' if there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

Example of an equation with 'One Solution':

Back

a = 7 (The solution is a = 7.)

Front

Example of an equation with 'No Solution':

Back

4y + 5 = 4y - 7 (This simplifies to 5 = -7, which is false.)

Front

Example of an equation with 'Infinitely Many Solutions':

Back

28a - 4 = 28a - 4 (This simplifies to 0 = 0, which is always true.)

Front

How can you identify an equation with 'No Solution'?

Back

If simplifying the equation leads to a false statement, such as 5 = -3.

Front

How can you identify an equation with 'Infinitely Many Solutions'?

Back

If simplifying the equation leads to a true statement, such as 0 = 0.

Front

What is the first step in solving an equation to find its solutions?

Back

Isolate the variable on one side of the equation.

Front

What is a common mistake when solving equations?

Back

Assuming that the variable can be canceled without considering the implications.