One Solution, No Solution, Infinite Solutions

Front

What does it mean when an equation has one solution?

Back

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

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values of the variable that can satisfy the equation, often resulting in a contradiction.

Front

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

Back

An equation has infinitely many solutions when any value of the variable satisfies the equation, typically occurring when the equation simplifies to a true statement.

Front

How do you determine if an equation has no solution?

Back

To determine if an equation has no solution, simplify the equation and look for a contradiction, such as a statement like 0 = 5.

Front

How do you determine if an equation has infinitely many solutions?

Back

To determine if an equation has infinitely many solutions, simplify the equation and find that both sides are equivalent, such as 0 = 0.

Front

What is the first step in solving a linear equation?

Back

The first step in solving a linear equation is to isolate the variable on one side of the equation.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and position of the line represented by the equation.

Front

What is a contradiction in the context of solving equations?

Back

A contradiction occurs when the simplification of an equation leads to an impossible statement, indicating no solution.

Front

What is the role of like terms in solving equations?

Back

Like terms can be combined to simplify an equation, making it easier to isolate the variable.

Front

What is the difference between a linear equation and a non-linear equation?

Back

A linear equation represents a straight line and has a degree of 1, while a non-linear equation can represent curves and has a degree greater than 1.