One Solution, No Solution, Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

What is the definition of one solution in the context of equations?

Back

Only this ONE solution will make the equation true.

Front

What does it indicate if an equation has infinite solutions?

Back

It indicates that there are an unlimited number of values for the variable that will satisfy the equation.

Front

How can you determine if an equation has no solution?

Back

If simplifying the equation leads to a contradiction, such as 0 = 5, it has no solution.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.

Front

What does the equation 8z - 22 = 3(3z + 11) - z simplify to?

Back

It simplifies to a contradiction, indicating no solution.

Front

What is the significance of the equation 3(x-2) + 1 = 3x - 5?

Back

It simplifies to an identity, indicating infinite solutions.

Front

What is a contradiction in the context of equations?

Back

A statement that is always false, such as 0 = 5, indicating no solution.

Front

What is an identity in the context of equations?

Back

A statement that is always true, indicating infinite solutions.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.