One, None, Infinite 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.

Front

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.

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, often because the equation simplifies to a true statement.

Front

Example of an equation with no solution: 2x + 3 = 2x + 5. What is the solution?

Back

No solution.

Front

Example of an equation with one solution: 3x + 4 = 10. What is the solution?

Back

x = 2.

Front

Example of an equation with infinitely many solutions: x + 2 = x + 2. What is the solution?

Back

Infinitely many solutions.

Front

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

Back

Simplify the equation as much as possible.

Front

If two equations are equivalent, what can be said about their solutions?

Back

They have the same solutions.

Front

What is the significance of the coefficients in a linear equation?

Back

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

Front

How can you tell if an equation has no solution by looking at its form?

Back

If simplifying leads to a contradiction, such as 0 = 5, it has no solution.