One Solution, No Solution, Many Solutions

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value of the variable that makes the equation true.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation.

Front

What does it mean if an equation has many solutions?

Back

An equation has many solutions when any value of the variable makes the equation true.

Front

Example of an equation with one solution: 5z = 25. What is the solution?

Back

z = 5.

Front

Example of an equation with no solution: 3z + 8 = 2 + 3z. Why does it have no solution?

Back

Both sides simplify to 8 = 2, which is false.

Front

Example of an equation with many solutions: Z = Z. Why does it have many solutions?

Back

Any value of Z satisfies the equation.

Front

What is the general form of an equation with one solution?

Back

An equation in the form of ax + b = c, where a ≠ 0.

Front

What is the general form of an equation with no solution?

Back

An equation that simplifies to a false statement, like 0 = 5.

Front

What is the general form of an equation with many solutions?

Back

An equation that simplifies to a true statement, like 0 = 0.

Front

How can you identify an equation with no solution?

Back

If the variable cancels out and you are left with a false statement.