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5-4 Elimination Using Multiplication aka Linear Combination Algebra 1 Glencoe McGraw-HillLinda Stamper

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Often the equations are not ready for one variable to cancel. You will need to create the opposites. Multiply one or both equations by a number to obtain coefficients that are opposites for one of the variables.

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Choose one of the variables to create an opposite. Multiply by a number needed to make one variable opposites. Add your equation because you now have opposites. Write solution as an ordered pair. (–1,2) original Substitute the solved value into either of the original equations to find the value for the other variable. Yeah a handout. I do not have to copy these notes in my notebook!

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(-1,2) While you can choose either of the variables to make opposites, choosing wisely may save you some work. Here is the work if the x variable is used to create the opposite.

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Example 1 Solve the linear system using elimination. Example 2

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Example 1 Solve the linear system. (2,2)

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Example 2 Solve the linear system. (–2,3)

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Example 2 Solve the linear system. (–2,3)

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Solving A Linear System By Elimination 1) Arrange the equations with like terms in columns. 2) Multiply, if necessary, one or both equations by the number needed to make one of the variables an opposite. 3) 3)Add the equations when one of the variables have opposites. Then solve. 4) 4)Substitute the value solved into either of the original equations and solve for the other variable. 5) 5)Check the ordered pair solution in each of the original equations.

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When solving a system by elimination, rearrange the terms so that the corresponding variables are vertically stacked. Substitute the solved value into either of the original equations. Write answer as an ordered pair. (0,2)

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Example 3 Solve the linear system using elimination. Example 4 Example 5 Example 6 Write a linear system and then solve. Five times the first number minus three times the second number is six. Two times the first number minus five times the second number is ten. Find the numbers. Assign labels. Translate each sentence. Solve the system. Write a sentence to give the answer.

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Example 3 Solve the linear system. (2,1) Rewrite in standard form.

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Example 4 Solve the linear system. Rewrite in standard form. (–1,3)

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Example 5 Solve the linear system.

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Example 6 Five times the first number minus 3 times the second number is six. Two times the first number minus five times the second number is 10. Find the numbers. Let x = first number Let y = second number Translate each sentence. Solve the system. Write a sentence to give the answer. The numbers are -2 and 0.

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Practice Problems 1) (2,0) 2) (1,–2) 3) 4) Six times the first number plus two times the second number is two. Four times the first number plus three times the second number is eight. Find the numbers. The numbers are -1 and 4.

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5-A6 Page 276-278 #7–17,30,34-36,44-48.

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