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Which of these strategies would eliminate a variable in the system of equations? {[-7x+2y=5],[3x-5y=-5]:} Choose 2 answers: A Multiply the top equation by 3 , multiply the bottom equation by 7 , then add the equations. B] Add the equations. c Multiply the top equation by 5 , multiply the bottom equation by 2 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{−7x+2y=53x−5y=−5 \left\{\begin{array}{l} -7 x+2 y=5 \\ 3 x-5 y=-5 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 33 , multiply the bottom equation by 77 , then add the equations.\newline(B) Add the equations.\newline(C) Multiply the top equation by 55 , multiply the bottom equation by 22 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{−7x+2y=53x−5y=−5 \left\{\begin{array}{l} -7 x+2 y=5 \\ 3 x-5 y=-5 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 33 , multiply the bottom equation by 77 , then add the equations.\newline(B) Add the equations.\newline(C) Multiply the top equation by 55 , multiply the bottom equation by 22 , then add the equations.
  1. Analyze system of equations: Analyze the given system of equations to determine which variable can be eliminated using the given strategies.\newlineThe system of equations is:\newline−7x+2y=5-7x + 2y = 5\newline3x−5y=−53x - 5y = -5
  2. Strategy A: Multiply and add equations: Consider strategy A: Multiply the top equation by 33, multiply the bottom equation by 77, then add the equations.\newlineMultiplying the top equation by 33 gives us:\newline−21x+6y=15-21x + 6y = 15\newlineMultiplying the bottom equation by 77 gives us:\newline21x−35y=−3521x - 35y = -35
  3. Check elimination of variable x: Add the equations from strategy A to see if a variable is eliminated.\newline(−21-21x + 66y) + (2121x - 3535y) = 1515 - 3535\newlineThe x terms cancel out, and we are left with:\newline66y - 3535y = −20-20\newline−29-29y = −20-20\newlineThis strategy eliminates the variable x.
  4. Strategy B: Add equations: Consider strategy B: Add the equations without any multiplication.\newline(−7x+2y)+(3x−5y)=5−5(-7x + 2y) + (3x - 5y) = 5 - 5\newline−7x+3x+2y−5y=0-7x + 3x + 2y - 5y = 0\newline−4x−3y=0-4x - 3y = 0\newlineThis strategy does not eliminate any variable, as both xx and yy are still present in the equation.
  5. No elimination of variables: Consider strategy C: Multiply the top equation by 55, multiply the bottom equation by 22, then add the equations.\newlineMultiplying the top equation by 55 gives us:\newline−35x+10y=25-35x + 10y = 25\newlineMultiplying the bottom equation by 22 gives us:\newline6x−10y=−106x - 10y = -10
  6. Strategy C: Multiply and add equations: Add the equations from strategy C to see if a variable is eliminated.\newline(−35x+10y)+(6x−10y)=25−10(-35x + 10y) + (6x - 10y) = 25 - 10\newlineThe y terms cancel out, and we are left with:\newline−35x+6x=15-35x + 6x = 15\newline−29x=15-29x = 15\newlineThis strategy eliminates the variable y.

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