Types of Solutions

Front

What is a solution in mathematics?

Back

A solution is a value or set of values that satisfy an equation.

Front

What does 'no solution' mean in an equation?

Back

No matter what constant is substituted in for the variable, the equation will NEVER be true.

Front

What does 'one solution' mean in an equation?

Back

Only this ONE solution will make the equation true.

Front

What does 'infinite solutions' mean in an equation?

Back

There are countless values that can satisfy the equation.

Front

How do you determine if an equation has no solution?

Back

If the equation simplifies to a false statement, like 0 = 5.

Front

How do you determine if an equation has one solution?

Back

If the equation simplifies to a true statement with a specific value for the variable.

Front

How do you determine if an equation has infinite solutions?

Back

If the equation simplifies to a true statement that is always valid, like 0 = 0.

Front

What is the equation for a line with infinite solutions?

Back

An example is 2x + 3 = 2(x + 1) + 1.

Front

What is the first step in solving an equation?

Back

Isolate the variable on one side of the equation.

Front

What is the importance of checking your solution?

Back

To ensure that the solution satisfies the original equation.