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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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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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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Back

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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CCSS.HSA.REI.C.9

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Back

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6