One, Infinite, No Solution

Front

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

Back

It means that there are an infinite number of values for the variable that satisfy the equation, often because the equation simplifies to a true statement (e.g., 0 = 0).

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, often because it simplifies to a false statement (e.g., 0 = 5).

Front

Solve: 6x - 9 = 3(2x - 3)

Back

Infinitely Many Solutions

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Simplify and determine the number of solutions: 3x - 7 = 3(x - 3) + 2

Back

Infinitely Many Solutions

Front

Determine the number of solutions for the equation: 5x - 10 = 5x + 10

Back

No Solution

Front

Solve: 2(3x - 5) = 6x - 10

Back

Infinitely Many Solutions

Front

What is a linear equation?

Back

An equation that can be written in the form ax + b = c, where a, b, and c are constants.

Front

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

Back

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

Front

What is the difference between one solution, no solution, and infinitely many solutions?

Back

One solution means a unique value satisfies the equation; no solution means no value satisfies it; infinitely many solutions mean many values satisfy it.