Special Cases for Equations

Front

What does it mean when an equation has no solution?

Back

The equation will NEVER be true when any value is substituted in for the variable.

Front

What does it mean when an equation has infinitely many solutions?

Back

The equation is always TRUE when any value is substituted in for the variable.

Front

Solve: 5x + 4 = 5x − 3

Back

No solutions.

Front

Solve: 9x + 7 − 5x = 4x − 7

Back

No solutions.

Front

Solve: 2y − 3 = 2y − 3

Back

Infinitely many solutions.

Front

What is a special case in equations?

Back

A situation where the equation does not behave as a typical linear equation, leading to no solutions or infinitely many solutions.

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

What is the difference between no solution and infinitely many solutions?

Back

No solution means the equation is never true, while infinitely many solutions mean the equation is always true.

Front

Solve: 3x + 5 = 3x + 5

Back

Infinitely many solutions.

Front

Solve: 4x + 2 = 4x + 3

Back

No solutions.