One Solution, No Solution, Many Solutions

Front

What is meant by 'One Solution' in an equation?

Back

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

Front

What does 'No Solution' mean in the context of equations?

Back

'No Solution' means that there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

Front

What does 'Many Solutions' indicate in an equation?

Back

'Many Solutions' indicates that there are infinitely many values of the variable that satisfy the equation, often when the equation simplifies to a true statement.

Front

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

Back

z = 5.

Front

Example of an equation with Many Solutions: 3z + 7 = 7 + 3z. What does this imply?

Back

This implies that the equation is true for all values of z.

Front

Example of an equation with No Solution: 18a + 45 = 18a - 37.2. What does this imply?

Back

This implies that the equation leads to a contradiction, such as 45 = -37.2.

Front

What is the first step to determine the number of solutions in an equation?

Back

The first step is to simplify the equation as much as possible.

Front

How can you tell if an equation has No Solution?

Back

An equation has No Solution if simplifying leads to a false statement, like 0 = 5.

Front

How can you tell if an equation has Many Solutions?

Back

An equation has Many Solutions if simplifying leads to a true statement, like 0 = 0.

Front

What is the significance of coefficients in determining solutions?

Back

Coefficients help identify if the terms can be combined or if they lead to contradictions.