How Many Solutions?

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value substituted for the variable makes the equation true.

Front

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

Back

By simplifying the equation and analyzing the resulting expressions. If they are equivalent, it has infinite solutions; if they contradict, it has no solution; if they yield a specific value, it has one solution.

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 the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line represented by the equation.

Front

What is the definition of a linear equation?

Back

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

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

What is the graphical representation of an equation with no solution?

Back

The graphical representation is two parallel lines that never intersect.

Front

What is the graphical representation of an equation with infinite solutions?

Back

The graphical representation is the same line drawn over itself.

Front

What is the importance of simplifying equations?

Back

Simplifying equations helps to clearly identify the relationship between variables and determine the number of solutions.