Elimination method word problems

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of equations by eliminating one variable, allowing for the solution of the remaining variable.

Front

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the problem accurately.

Front

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

Back

To eliminate a variable means to manipulate the equations so that one variable cancels out, making it possible to solve for the other variable.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

How can you check the solution of a system of equations?

Back

Substitute the values of the variables back into the original equations to verify that both equations hold true.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that the coefficients of one variable are opposites.

Front

In the equation 4x + 6y = 13, what do x and y represent?

Back

In this context, x and y typically represent quantities of items being purchased, such as apples and bananas.

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What is the significance of the coefficients in a system of equations?

Back

Coefficients represent the rate or quantity of each variable in the context of the problem, affecting the total outcome.

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How do you interpret the solution of a system of equations graphically?

Back

The solution represents the point where the graphs of the equations intersect, indicating the values of the variables that satisfy both equations.

Front

What is a common mistake when setting up equations from word problems?

Back

A common mistake is misinterpreting the relationships or conditions described in the problem, leading to incorrect equations.