Special Case Equations

Front

What is a special case equation?

Back

A special case equation is an equation that has either no solution, infinitely many solutions, or a unique solution, depending on the relationship between the variables.

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, indicating 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, indicating that the two sides are equivalent for all values.

Front

Solve the equation: -2x + 6 = 2x - 6

Back

x = 3

Front

Solve the equation: 2x + 19 = 2x + 19

Back

Infinitely many solutions.

Front

Solve the equation: 6x + 2 = 6x + 2

Back

Infinitely many solutions.

Front

Solve the equation: x + 19 = x - 1

Back

No solution.

Front

Solve the equation: 7x + 1 = 6x + 8

Back

x = 7

Front

What is the first step in solving linear equations?

Back

The first step is to isolate the variable on one side of the equation.

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the rate of change of the variable and influence the slope of the line represented by the equation.