One Solution, No Solution, Infinite Solutions

Front

What does 'one solution' mean in the context of equations?

Back

An equation has 'one solution' when there is exactly one value of the variable that satisfies the equation.

Front

What does 'no solution' mean in the context of equations?

Back

An equation has 'no solution' when there are no values of the variable that can satisfy the equation.

Front

What does 'infinite solutions' mean in the context of equations?

Back

An equation has 'infinite solutions' when there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

Example of an equation with one solution: Solve for x: 2x + 3 = 7

Back

x = 2

Front

Example of an equation with no solution: Solve for x: 2x + 3 = 2x - 5

Back

No solution.

Front

Example of an equation with infinite solutions: Solve for x: 3(x + 2) = 3x + 6

Back

Infinite 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 an equation simplifies to a statement like 0 = 0, what does that indicate?

Back

It indicates that there are infinite solutions.

Front

If an equation simplifies to a statement like 5 = 3, what does that indicate?

Back

It indicates that there is no solution.

Front

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

Back

Coefficients help identify relationships between variables; if they are equal in a linear equation, it may lead to infinite solutions.