No Solution/Infinite Solution/One Solution

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, often resulting in a contradiction.

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, typically when both sides of the equation are equivalent.

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.

Front

Solve for x: 4x - 9 = 3.5x - 9

Back

x = 0

Front

Determine the number of solutions: 2(15c + 8) = 9(2c + 4) - (3c + 2)

Back

One Solution

Front

Determine the number of solutions: 6x - 18 = 4(2x - 3) - (2x + 6)

Back

Infinite Solution

Front

Solve for x: 2(4x - 1) = 3(x + 2)

Back

x = 1.6

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when an equation simplifies to a false statement, indicating no solutions exist.

Front

What is a dependent equation?

Back

A dependent equation is one that has infinitely many solutions, as it represents the same line in a graph.

Front

What is an independent equation?

Back

An independent equation is one that has exactly one solution, representing two intersecting lines in a graph.