One, No, Infinitely Many Solutions Flashcard

Front

What does it mean if an equation has infinitely many solutions?

Back

The equation is true for all values of the variable, meaning both sides of the equation are identical.

Front

What does it mean if an equation has no solution?

Back

The equation is contradictory, meaning there are no values of the variable that can satisfy it.

Front

What is an example of an equation with infinitely many solutions?

Back

7x - 1 = 7x - 1.

Front

What is an example of an equation with no solution?

Back

7x - 3 = 7x + 3.

Front

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

Back

Simplify both sides of the equation as much as possible.

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the relationship between the variables and can affect the number of solutions.

Front

How can you tell if two equations are equivalent?

Back

If they simplify to the same expression, they are equivalent and have infinitely many solutions.

Front

What is a linear equation?

Back

An equation that can be written in the form ax + b = c, where a, b, and c are constants.

Front

What is the solution set of an equation?

Back

The set of all values that satisfy the equation.

Front

What does it mean if an equation has one solution?

Back

There is exactly one value of the variable that makes the equation true.