Systems of Linear Equations

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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 does it mean to solve a system of linear equations?

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To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the substitution method?

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

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is the elimination method?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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What is graphing in the context of systems of linear equations?

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Graphing involves plotting the equations on a coordinate plane and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

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What is an ordered pair?

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An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

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CCSS.5.G.A.1

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What does it mean for an equation to be in standard form?

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An equation is in standard form if it is written as Ax + By = C, where A, B, and C are integers, and A is non-negative.

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What is an isolated variable?

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An isolated variable is a variable that is expressed alone on one side of the equation, making it easier to substitute into another equation.

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CCSS.HSA.CED.A.4

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What is the first step in solving a system by substitution?

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The first step is to make sure one of the equations has an isolated variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What are the three methods for solving systems of linear equations?

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The three methods are graphing, substitution, and elimination.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6