One Solution, No Solution, or Infinite Solutions

Front

What does it mean for an equation to have 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 for an equation to have no solution?

Back

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

Front

What does it mean for an equation to have infinite solutions?

Back

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

Front

How can you determine if an equation has one, no, or infinite solutions?

Back

You can determine this by simplifying the equation and analyzing the resulting expressions for contradictions or identities.

Front

What is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation.

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when simplifying an equation leads to a false statement, indicating that no solutions exist.

Front

What is an identity in the context of equations?

Back

An identity is an equation that is true for all values of the variable, indicating that there are infinite solutions.

Front

What is the significance of coefficients in linear equations?

Back

Coefficients determine the slope and position of the line represented by the equation, affecting the number of solutions.

Front

What role do constants play in linear equations?

Back

Constants shift the graph of the equation up or down, influencing the intersection points with the axes.

Front

How do you simplify the equation 3x - 7 = 3(x - 3) + 2?

Back

Distributing gives 3x - 7 = 3x - 9 + 2, which simplifies to 3x - 7 = 3x - 7, indicating infinite solutions.