Solving Systems of Equations By Elimination

Front

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

When using the elimination method, what is the goal?

Back

The goal is to eliminate one variable so that you can solve for the other variable in the system of equations.

Front

How do you determine which variable to eliminate in a system of equations?

Back

You can determine which variable to eliminate by looking for coefficients that are opposites or can be made opposites through multiplication.

Front

What does it mean to eliminate a variable?

Back

To eliminate a variable means to manipulate the equations so that one variable is removed, allowing for the solution of the remaining variable.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate.

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What happens if the coefficients of the variable you want to eliminate are not opposites?

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If the coefficients are not opposites, you can multiply one or both equations by a number to create opposites.

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What is the result of eliminating a variable from a system of equations?

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The result is a single equation with one variable, which can be solved to find the value of that variable.

Front

In the equation -7x - y = 9 and 3x + y = -5, what is the equation after eliminating the y terms?

Back

The equation after eliminating the y terms is -4x = 4.

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In the equation -9x - 4y = -20 and 5x + 4y = 4, what is the equation after eliminating the y terms?

Back

The equation after eliminating the y terms is -4x = -16.

Front

What is the significance of opposite signs in the elimination method?

Back

Opposite signs allow for easy elimination of variables when the equations are added together.