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 that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean if an equation has one solution?

Back

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

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value satisfies the equation, often resulting in equivalent expressions.

Front

Simplify: 3x - 8 = 3(x - 4) + 1. What is the solution?

Back

No solutions.

Front

Simplify: 3(x-2) + 1 = 3x - 5. What is the solution?

Back

Infinite solutions.

Front

How many solutions does the equation 6m + 18 = 2m + 18 have?

Back

One solution.

Front

What is the missing information that would make the statement true for infinite solutions: _ + 10 = 5x + 10?

Back

5x.

Front

What is the solution to the equation 2x + 3 = 2x + 5?

Back

No solution.

Front

What is a contradiction in an equation?

Back

A contradiction occurs when simplifying an equation leads to a false statement, indicating no solutions.

Front

What is a dependent system of equations?

Back

A dependent system has infinite solutions because the equations represent the same line.