1.4

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School

University of California, Berkeley *

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N54

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Mathematics

Date

Apr 3, 2024

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docx

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2

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Question and Solution Template Learning Attribute(s) Included in Question : 1.4.8 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Calculator Active? No Question : What value of x satisfies the system of equations: y = x 2 and y = 2 x 1 . A) 0 B) 1 C) 2 D) 3 Correct Answer: B Equation Upload (Please write the text of the question along with the LaTeX Code): What value of $x$ satisfies the system of equations:$y=x^{2}$ and $y=2x-1$ A) $0$
B) $1$ C) $2$ D) $3$ On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult): 8 i Solution : Step 1 : Substitute y = x 2 into the second equation. x 2 = 2 x 1 x 2 2 x + 1 = 0 Using ( a b ) 2 formula and solve for x . x 2 2. x .1 + 1 2 = 0 ( x 1 ) 2 = 0 ( x 1 ) = 0 x = 1 Equation Upload (Please write the text of the question along with the LaTeX Code): \textbf{Step 1}: Substitute $y=x^2$ into the second equation. $$x^2=2x-1$$ $$x^2-2x+1=0$$ Using $(a-b)^{2}$ formula and solve for $x$. $$x^2-2.x.1+1^2=0$$ $$(x-1)^{2}=0$$ $$(x-1)=0$$ $$x=1$$
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