One Solution, No Solution, Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when simplifying leads to a contradiction, such as 0 = 1.

Front

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

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation. This typically happens when both sides of the equation simplify to the same expression.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation. This is the most common case in linear equations.

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

Solve: 3(x-2) + 1 = 3x - 5

Back

Infinitely Many Solutions

Front

Solve: 6x + 9 – x = 3x + 9 + x

Back

One Solution

Front

Solve: 3x - 8 = 3(x - 4) + 1

Back

No Solutions

Front

What is a contradiction in an equation?

Back

A contradiction occurs when the simplification of an equation leads to a false statement, indicating that no solutions exist.

Front

What is a dependent equation?

Back

A dependent equation is one that has infinitely many solutions, meaning the equations represent the same line when graphed.