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Which of these strategies would eliminate a variable in the system of equations? {[x-2y=11],[5x+3y=-11]:} Choose 1 answers: A Multiply the top equation by 5 , then add the equations. B Add the equations. C Multiply the top equation by -5 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{x−2y=115x+3y=−11 \left\{\begin{array}{l} x-2 y=11 \\ 5 x+3 y=-11 \end{array}\right. \newlineChoose 11 answers:\newline(A) Multiply the top equation by 55 , then add the equations.\newline(B) Add the equations.\newline(C) Multiply the top equation by −5-5 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{x−2y=115x+3y=−11 \left\{\begin{array}{l} x-2 y=11 \\ 5 x+3 y=-11 \end{array}\right. \newlineChoose 11 answers:\newline(A) Multiply the top equation by 55 , then add the equations.\newline(B) Add the equations.\newline(C) Multiply the top equation by −5-5 , then add the equations.
  1. Analyze coefficients: Analyze the coefficients of the variables in both equations to determine which variable can be eliminated with the least amount of manipulation.\newlineThe first equation is x−2y=11x - 2y = 11 and the second equation is 5x+3y=−115x + 3y = -11. To eliminate a variable, we need to make the coefficients of either xx or yy opposites in both equations.
  2. Evaluate option A: Evaluate option A: Multiply the top equation by 55, then add the equations.\newlineIf we multiply the first equation by 55, we get 5(x−2y)=5(11)5(x - 2y) = 5(11), which simplifies to 5x−10y=555x - 10y = 55. Adding this to the second equation (5x+3y=−11)(5x + 3y = -11) would not eliminate any variable because the coefficients of xx are the same and the coefficients of yy are not opposites.
  3. Evaluate option B: Evaluate option B: Add the equations.\newlineIf we add the equations as they are, we get (x−2y)+(5x+3y)=11−11(x - 2y) + (5x + 3y) = 11 - 11, which simplifies to 6x+y=06x + y = 0. This does not eliminate any variable.
  4. Evaluate option C: Evaluate option C: Multiply the top equation by −5-5, then add the equations.\newlineIf we multiply the first equation by −5-5, we get −5(x−2y)=−5(11)-5(x - 2y) = -5(11), which simplifies to −5x+10y=−55-5x + 10y = -55. Adding this to the second equation (5x+3y=−11)(5x + 3y = -11) would eliminate the variable xx because the coefficients of xx are now opposites.
  5. Perform operation from option C: Perform the operation from option C to confirm that it eliminates the variable xx.(−5x+10y)+(5x+3y)=−55−11,(-5x + 10y) + (5x + 3y) = -55 - 11, which simplifies to 0x+13y=−660x + 13y = -66. The variable xx has been eliminated, confirming that option C is the correct strategy.

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