Linear Systems Substitution Method

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What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

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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 equations?

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To solve a system of 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

Front

What is the substitution method?

Back

The substitution method is a technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

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How do you determine if a point is a solution to a system of equations?

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A point is a solution if it satisfies all equations in the system when the coordinates are substituted into the equations.

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What is the first step in using the substitution method?

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The first step is to solve one of the equations for one variable in terms of the other variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has no solution?

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It means that the lines represented by the equations are parallel and never intersect.

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CCSS.8.EE.C.8A

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What does it mean if a system of equations has infinitely many solutions?

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It means that the equations represent the same line, and there are countless points that satisfy both equations.

Tags

CCSS.8.EE.C.8A

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What is the purpose of substituting one equation into another?

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The purpose is to reduce the number of variables and simplify the problem to find the solution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the result of substituting y=4x-1 into y=2x-5?

Back

You get the equation 4x-1=2x-5, which can be solved for x.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the point of intersection in a linear system?

Back

The point of intersection represents the solution to the system, where both equations are satisfied.

Tags

CCSS.8.EE.C.8B