FM 3.5 Solving Systems of Equations by Elimination

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What is a system of equations?

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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 in the system.

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

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

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What is the elimination method?

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The elimination method is a technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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

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It is necessary to multiply an equation when the coefficients of the variable to be eliminated are not opposites or do not match.

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What is the first step in the elimination method?

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

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How do you determine which variable to eliminate?

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

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What is the purpose of multiplying both equations by different numbers?

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Multiplying both equations by different numbers helps to create equal or opposite coefficients for the variable to be eliminated.

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What does it mean if two equations are dependent?

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Dependent equations are equations that represent the same line, meaning they have infinitely many solutions.

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What does it mean if two equations are independent?

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Independent equations are equations that represent different lines, meaning they have exactly one solution.

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What does it mean if two equations are inconsistent?

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Inconsistent equations are equations that represent parallel lines, meaning they have no solution.