Solving Special Systems of Linear Equations Flashcard

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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What are the three main methods to solve systems of linear equations?

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The three main methods are: 1) Substitution method, 2) Elimination method, 3) Graphing.

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When is the elimination method preferred over substitution?

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The elimination method is preferred when the coefficients of the variables are easy to manipulate, allowing for quick elimination of one variable.

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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Add the two equations to eliminate y: 3x = 11, so x = 11/3. Substitute x back to find y.

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Subtract the second equation from the first to eliminate x: 4y = 10, so y = 2. Substitute y back to find x.

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Substitute x in the second equation: 5y + y = 6, so 6y = 6, thus y = 1. Substitute y back to find x.

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