How Many Solutions?

Front

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

Back

It means that there are countless values for the variable that satisfy the equation, often because the equation simplifies to a true statement (e.g., 0 = 0).

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy both equations.

Front

What is a unique solution in the context of equations?

Back

A unique solution means there is exactly one set of values for the variables that satisfies the equation.

Front

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

Back

Infinitely Many Solutions

Front

Solve: 3(x-2) + 1 = 3x - 5

Back

Infinitely Many Solutions

Front

How can you tell if a system of equations has no solution?

Back

If the equations simplify to a contradiction, such as 0 = 5, the system has no solution.

Front

Solve: 4(x - 5) + 3 = 2(2x + 9)

Back

No Solution

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The graphs of the equations overlap completely, representing the same line.

Front

What is the graphical representation of a system with no solution?

Back

The graphs of the equations are parallel lines that do not intersect.