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.

Front

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 elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for easier solving 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 all the fractions present.

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.

Front

Back

Front

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

Back

The first step is to align the equations and decide which variable to eliminate, then manipulate the equations accordingly.

Front

What happens when you multiply an entire equation by a constant?

Back

Multiplying an entire equation by a constant does not change the solution of the equation, but it can make calculations easier.

Front

What is the purpose of adding equations in the elimination method?

Back

Adding equations can help eliminate one of the variables, simplifying the system and making it easier to solve.

Front

What is a coefficient in an equation?

Back

A coefficient is a numerical factor that multiplies a variable in an equation, indicating how many times the variable is counted.