FM 3.5 Solving Systems of Equations by Elimination

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What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations (by multiplying or rearranging) so that when added or subtracted, one variable cancels out.

Front

When is it necessary to multiply an equation in the elimination method?

Back

It is necessary to multiply an equation when the coefficients of the variable to be eliminated are not the same or do not allow for easy cancellation.

Front

What does it mean to 'eliminate' a variable?

Back

To 'eliminate' a variable means to remove it from the equations, allowing you to solve for the remaining variable.

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How do you determine which variable to eliminate?

Back

Choose the variable that can be easily eliminated based on the coefficients in the equations.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What is the goal of solving a system of equations?

Back

The goal is to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is a coefficient in an equation?

Back

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

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution set.

Front

What is the significance of the solution to a system of equations?

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The solution represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.