Solving Linear Equations with Substitution

This video tutorial explains how to solve systems of linear equations using the substitution method. It covers the basic concept, provides step-by-step examples, and discusses different outcomes such as one solution, no solution, and infinitely many solutions. The tutorial emphasizes the importance of substitution in simplifying systems to a single variable equation, making it easier to solve.

What is the main reason for using the substitution method instead of graphing?

• It is more accurate.

• It is faster.

• It is easier to understand.

• Graphing is sometimes impractical.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

In the first example, what is the value of x after performing the substitution?

• 3

• 0

• 1

• 2

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CCSS.6.EE.A.2C

After finding x = 1 in the first example, what is the value of y?

• 4

• 3

• 2

• 1

In the second example, what is the first step to solve the system of equations?

• Solve the second equation for y.

• Solve the first equation for y.

• Solve the second equation for x.

• Solve the first equation for x.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the value of y in the second example after solving the equation?

• 5

• 2

• 4

• 3

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CCSS.7.EE.B.4A

In the third example, what indicates that the system has no solution?

• The variables cancel out and we get a true statement.

• The variables cancel out and we get a false statement.

• The equations are parallel.

• The equations are identical.

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CCSS.8.EE.C.8B

What is the result when the variables cancel out in the third example?

• 11 = 11

• 11 = 10

• 10 = 11

• 10 = 10

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CCSS.8.EE.C.7A

In the fourth example, what is the first step to solve the system?

• Solve the second equation for y.

• Solve the first equation for y.

• Solve the second equation for x.

• Solve the first equation for x.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What indicates that the system has infinitely many solutions in the fourth example?

• The variables cancel out and we get a true statement.

• The variables cancel out and we get a false statement.

• The equations are parallel.

• The equations are identical.

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CCSS.8.EE.C.8B

What is the true statement obtained in the fourth example?

• Negative one equals negative one

• 2 = 2

• 1 = 1

• 0 = 0

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CCSS.8.EE.C.7A