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University of California, Berkeley *

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Mathematics

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Apr 3, 2024

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docx

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Question and Solution Template Learning Attribute(s) Included in Question : 1.4.6 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Calculator Active? No Question : System A : − 4 x − 6 y = 9 3 x + y =− 4 System : − 4 x − 6 y = 9 − x − 5 y = 5 How can we get System B from System A ? A) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations B) Replace one equation with the sum/difference of both equations C) Swap only the right-hand sides of both equations D) Swap the order of the equations Correct answer: B

Equation Upload (Please write the text of the question along with the LaTeX Code): System A: $-4x -6y=9$ $3x+y=-4$ System B : $-4x -6y=9$ $-x-5y=5$ How can we get System B from System A? A) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations B) Replace one equation with the sum/difference of both equations C) Swap only the right-hand sides of both equations D) Swap the order of the equations On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult): 4 i Solution : Step 1 : Sum the equations in System A. − x − 5 y = 5 Replacing the second equation in System A with this new equation, we get a system that's equivalent to System A : − 4 x − 6 y = 9 − x − 5 y = 5

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