One Solution, No Solution, Infinite Solutions

Front

What does it mean for an equation to have one solution?

Back

Only this ONE solution will make the equation true.

Front

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

Back

No matter what constant is substituted in for the variable, the equation will NEVER be true.

Front

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

Back

There are infinitely many values for the variable that will satisfy the equation.

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.

Front

What is the first step in solving the equation 3x - 7 = 3(x - 3) + 2?

Back

Distribute the 3 on the right side of the equation.

Front

What is the result of simplifying the equation 3x - 7 = 3(x - 3) + 2?

Back

The equation simplifies to 3x - 7 = 3x - 7, indicating infinite solutions.

Front

What is an example of an equation with no solution?

Back

An example is 2x + 3 = 2x + 5.

Front

What is an example of an equation with one solution?

Back

An example is 2x + 3 = 7.

Front

What is an example of an equation with infinite solutions?

Back

An example is 4x - 8 = 4(x - 2).

Front

What is the significance of the coefficients in determining the number of solutions?

Back

If the coefficients of the variables are the same and the constants are different, there is no solution.