Determine Number of Solutions

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, meaning the two sides of the equation are equivalent for all values of the variable.

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How can you determine if an equation has infinite solutions?

Back

To determine if an equation has infinite solutions, simplify the equation and check if it reduces to a true statement (e.g., 0=0) for all values of the variable.

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What is the significance of equivalent equations in solving for solutions?

Back

Equivalent equations have the same solution set, meaning if two equations are equivalent, they will yield the same values for the variable.

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.

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What does it mean for an equation to be an identity?

Back

An identity is an equation that is true for all values of the variable, indicating that the two sides of the equation are always equal.

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What is the difference between a unique solution and infinite solutions?

Back

A unique solution means there is exactly one value of the variable that satisfies the equation, while infinite solutions mean any value of the variable satisfies the equation.

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What is a contradiction in the context of equations?

Back

A contradiction occurs when an equation simplifies to a false statement (e.g., 0=5), indicating that there are no solutions.

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How do you simplify an equation to check for infinite solutions?

Back

To simplify an equation, combine like terms, distribute, and isolate the variable to see if it leads to a true statement.

Front

What role do coefficients play in determining the number of solutions of an equation?

Back

Coefficients affect the slope and position of the lines represented by the equations; if they are proportional, the equations may have infinite solutions.

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What is the importance of checking your work when solving equations?

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Checking your work ensures that the solution is correct and that no mistakes were made during the solving process.