No Solution, One Solution, Infinite Solutions

Front

What does it mean when an equation has 'One Solution'?

Back

An equation has 'One Solution' when there is exactly one value of the variable that satisfies the equation.

Front

What does it mean when 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.

Front

What does it mean when 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.

Front

How can you identify an equation with 'No Solution'?

Back

An equation can be identified as having 'No Solution' if simplifying it leads to a false statement, such as 0 = 5.

Front

How can you identify an equation with 'Infinite Solutions'?

Back

An equation can be identified as having 'Infinite Solutions' if simplifying it leads to a true statement, such as 0 = 0.

Front

What is the first step in solving a linear equation?

Back

The first step in solving a linear equation is to isolate the variable on one side of the equation.

Front

What is the significance of coefficients in linear equations?

Back

Coefficients are the numerical factors that multiply the variables in an equation, affecting the slope and position of the line represented by the equation.

Front

What role do constants play in linear equations?

Back

Constants are the fixed values in an equation that do not change, influencing the y-intercept of the line.

Front

What is the process of checking the solution of an equation?

Back

The process of checking the solution involves substituting the solution back into the original equation to verify if both sides are equal.

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when an equation simplifies to a statement that is always false, indicating 'No Solution'.