One Solution, No Solution, or Infinite Solutions

Front

What does it mean if an equation has one solution?

Back

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

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values of the variable that can satisfy the equation, often resulting in a contradiction.

Tags

CCSS.8.EE.C.7A

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

Tags

CCSS.8.EE.C.7A

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Tags

CCSS.8.EE.C.7A

Front

Solve: -5(2x - 4) = 2(10 - 5x)

Back

Infinite Solutions

Tags

CCSS.8.EE.C.7A

Front

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

Back

Infinitely Many Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve: 6x + 9 – x = 3x + 9 + x

Back

One 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 exist.

Tags

CCSS.8.EE.C.7A

Front

What is a dependent equation?

Back

A dependent equation is one that has infinite solutions, meaning the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

What is an independent equation?

Back

An independent equation has exactly one solution, meaning the lines represented by the equations intersect at one point.

Tags

CCSS.8.EE.C.8A