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Which of these strategies would eliminate a variable in the system of equations? {[6x+5y=1],[6x-5y=7]:} Choose 2 answers: A Multiply the top equation by 7 , then subtract the bottom equation from the top equation. B Subtract the bottom equation from the top equation. c Add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{6x+5y=16x−5y=7 \left\{\begin{array}{l} 6 x+5 y=1 \\ 6 x-5 y=7 \end{array}\right. \newlineChoose 22 answers:\newlineA Multiply the top equation by 77 , then subtract the bottom equation from the top equation.\newlineB Subtract the bottom equation from the top equation.\newlineC\newlineAdd the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{6x+5y=16x−5y=7 \left\{\begin{array}{l} 6 x+5 y=1 \\ 6 x-5 y=7 \end{array}\right. \newlineChoose 22 answers:\newlineA Multiply the top equation by 77 , then subtract the bottom equation from the top equation.\newlineB Subtract the bottom equation from the top equation.\newlineC\newlineAdd the equations.
  1. Analyze the system: Analyze the given system of equations to determine which strategies could eliminate a variable.\newlineThe system of equations is:\newline6x+5y=16x + 5y = 1\newline6x−5y=76x - 5y = 7\newlineWe need to find strategies that will eliminate either 'xx' or 'yy'.
  2. Evaluate option A: Evaluate option A: Multiply the top equation by 77, then subtract the bottom equation from the top equation.\newlineMultiplying the top equation by 77 gives us:\newline42x+35y=742x + 35y = 7\newlineNow, if we subtract the bottom equation (6x−5y=7)(6x - 5y = 7) from this new equation, we will not eliminate any variable because the coefficients of 'xx' and 'yy' in the new equation and the bottom equation are not opposites.
  3. Evaluate option B: Evaluate option B: Subtract the bottom equation from the top equation.\newlineSubtracting the bottom equation from the top equation gives us:\newline(6x+5y)−(6x−5y)=1−7(6x + 5y) - (6x - 5y) = 1 - 7\newlineThis simplifies to:\newline6x+5y−6x+5y=−66x + 5y - 6x + 5y = -6\newlineWhich further simplifies to:\newline10y=−610y = -6\newlineThis strategy successfully eliminates the variable ′x′'x'.
  4. Evaluate option C: Evaluate option C: Add the equations.\newlineAdding the equations gives us:\newline(6x+5y)+(6x−5y)=1+7(6x + 5y) + (6x - 5y) = 1 + 7\newlineThis simplifies to:\newline12x=812x = 8\newlineThis strategy successfully eliminates the variable ′y′'y'.

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