Flashcard 4.2

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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What does it mean to eliminate a variable in a system of equations?

Back

Eliminating a variable means manipulating the equations to remove one variable, making it easier to solve for the remaining variable.

Front

What is the purpose of multiplying equations in a system?

Back

Multiplying equations can help align coefficients of variables, allowing for easier elimination when adding or subtracting the equations.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variable.

Front

How do you clear fractions in an equation?

Back

To clear fractions, multiply every term in the equation by the least common denominator (LCD) of the fractions.

Front

What is the least common denominator (LCD)?

Back

The least common denominator is the smallest multiple that is common to the denominators of two or more fractions.

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Back

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations so that the coefficients of one variable can be easily manipulated for elimination.

Front

What does it mean to add equations in a system?

Back

Adding equations combines the left-hand sides and the right-hand sides, which can help eliminate a variable if the coefficients are aligned.

Front

What is a coefficient in an equation?

Back

A coefficient is a numerical factor that multiplies a variable in an equation.