Solving Systems of Equations with Linear Combinations

The video tutorial explains how to solve systems of equations using the linear combination method. It covers the basics of systems of equations, introduces the linear combination method, and demonstrates how to use addition, subtraction, and multiplication to eliminate variables and find solutions. The tutorial also provides examples and emphasizes the importance of checking solutions.

What are the three methods for solving systems of equations?

• Graphing, substitution, and division

• Graphing, substitution, and linear combinations

• Addition, subtraction, and multiplication

• Linear combinations, matrix, and graphing

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What is the purpose of the linear combination method?

• To graph the equations

• To find the highest common factor

• To complicate the equations

• To eliminate one variable

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When is it ideal to use the linear combination method?

• When variables cannot be eliminated

• When equations are in different forms

• When like terms are aligned

• When equations are in fraction form

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CCSS.8.EE.C.8B

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What is the result of adding two equations where the y terms are opposites?

• No variables are eliminated

• The x variable is eliminated

• Both variables are eliminated

• The y variable is eliminated

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CCSS.8.EE.C.8B

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Why might you subtract one equation from another in a system of equations?

• To eliminate both variables

• To simplify the equations

• To eliminate the y variable

• To eliminate the x variable

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What do you do if adding or subtracting the equations does not eliminate a variable?

• Substitute variables

• Graph the equations

• Divide the equations

• Multiply the equations

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What happens when you multiply both sides of an equation by the same number?

• Only the y variable is affected

• Only the x variable is affected

• The equation remains balanced

• The equation becomes unbalanced

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What is the least common multiple of 3 and 4, used to eliminate a variable through multiplication?

• 7

• 24

• 12

• 6

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How do you check if your solution to a system of equations is correct?

• Multiply the solutions

• Substitute the values back into both equations

• Substitute the values back into one equation

• Graph the solutions

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CCSS.8.EE.C.8B

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What is the result of multiplying an equation by a negative number?

• Halving the value of all coefficients

• Doubling the value of all coefficients

• Eliminating all variables

• Changing the sign of all terms