Determine How Many Solutions

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation. For example, the equation 4=8 has no solution.

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What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that satisfies the equation. For example, if you solve x=0, it has one solution.

Front

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

Back

It means that there are countless values for the variable that satisfy the equation. For example, the equation 5x + 4 = 5x + 4 has infinitely many solutions.

Front

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

Back

The first step is to simplify the equation as much as possible, combining like terms and isolating the variable.

Front

How can you tell if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

Front

What is an example of an equation with no solution?

Back

Front

What is an example of an equation with one solution?

Back

Front

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

Back

Front

What is the significance of the variable in an equation?

Back

The variable represents an unknown value that we are trying to solve for in the equation.

Front

What does it mean to isolate the variable in an equation?

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.