One Solution, No Solution, or 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, meaning the lines represented by the equations are parallel and never intersect.

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, meaning the lines represented by the equations intersect at exactly one point.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value satisfies the equation, meaning the lines represented by the equations are the same line.

Front

Solve: 8z - 22 = 3(3z + 11) - z

Back

No Solution

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

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

Back

No Solution

Front

Solve: 12(x + 3) = 4(2x + 9) + 4x

Back

Infinite Solutions

Front

What is the first step to determine if an equation has no solution?

Back

Simplify both sides of the equation and check if the resulting equation leads to a contradiction.

Front

What is the first step to determine if an equation has one solution?

Back

Simplify the equation and isolate the variable to find a specific value.

Front

What is the first step to determine if an equation has infinite solutions?

Back

Simplify the equation and check if both sides are identical after simplification.