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 solutions?

Back

The equation is contradictory and cannot be true for any value of the variable.

Front

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

Back

No matter what constant is substituted in for the variable, the equation is ALWAYS true.

Front

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

Back

By simplifying the equation and analyzing the resulting statements.

Front

What is the first step in solving the equation 3x - 8 = 3(x - 4) + 1?

Back

Distribute the 3 on the right side of the equation.

Front

What is the result of simplifying the equation 4x - 7 = 3(2x - 3) + 2 - 2x?

Back

The equation simplifies to a true statement, indicating infinite solutions.

Front

What is the significance of the coefficients in an equation when determining the number of solutions?

Back

The relationship between the coefficients can indicate whether the lines represented by the equations are parallel, intersecting, or the same line.

Front

What is the solution to the equation 12(x + 3) = 4(2x + 9) + 5x?

Back

x = 0.

Front

What is a contradictory equation?

Back

An equation that has no solutions because it leads to a false statement.

Front

What is a dependent equation?

Back

An equation that has infinite solutions because it represents the same line as another equation.