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Which of these strategies would eliminate a variable in the system of equations? {[2x+8y=-3],[3x+6y=-4]:} Choose 2 answers: A Multiply the top equation by 3 , multiply the bottom equation by -2 , then add the equations. B Multiply the top equation by 3 , multiply the bottom equation by 4 , then subtract the bottom equation from the top equation. c Multiply the top equation by -4 , multiply the bottom equation by 3 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{2x+8y=−33x+6y=−4 \left\{\begin{array}{l} 2 x+8 y=-3 \\ 3 x+6 y=-4 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 33 , multiply the bottom equation by −2-2 , then add the equations.\newline(B) Multiply the top equation by 33 , multiply the bottom equation by 44 , then subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by −4-4 , multiply the bottom equation by 33 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{2x+8y=−33x+6y=−4 \left\{\begin{array}{l} 2 x+8 y=-3 \\ 3 x+6 y=-4 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 33 , multiply the bottom equation by −2-2 , then add the equations.\newline(B) Multiply the top equation by 33 , multiply the bottom equation by 44 , then subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by −4-4 , multiply the bottom equation by 33 , then add the equations.
  1. Analyze and Determine Elimination: Analyze the given system of equations to determine how to eliminate a variable.\newlineThe system of equations is:\newline{2x+8y=−33x+6y=−4 \begin{cases} 2x + 8y = -3 \\ 3x + 6y = -4 \end{cases} \newlineTo eliminate a variable, we need to make the coefficients of either x or y in both equations the same with opposite signs so that when we add or subtract the equations, one of the variables cancels out.
  2. Apply Strategy A: Apply strategy A to see if it eliminates a variable.\newlineStrategy A involves multiplying the top equation by 33 and the bottom equation by −2-2. Let's do the calculations:\newlineTop equation after multiplying by 33:\newline3(2x)+3(8y)=3(−3) 3(2x) + 3(8y) = 3(-3) \newline6x+24y=−9 6x + 24y = -9 \newlineBottom equation after multiplying by −2-2:\newline−2(3x)+−2(6y)=−2(−4) -2(3x) + -2(6y) = -2(-4) \newline−6x−12y=8 -6x - 12y = 8 \newlineNow, add the modified equations:\newline(6x+24y)+(−6x−12y)=−9+8 (6x + 24y) + (-6x - 12y) = -9 + 8 \newline6x−6x+24y−12y=−1 6x - 6x + 24y - 12y = -1 \newline0x+12y=−1 0x + 12y = -1 \newlineThe x variable is eliminated.
  3. Apply Strategy C: Apply strategy C to see if it eliminates a variable.\newlineStrategy C involves multiplying the top equation by −4-4 and the bottom equation by 33. Let's do the calculations:\newlineTop equation after multiplying by −4-4:\newline−4(2x)+−4(8y)=−4(−3) -4(2x) + -4(8y) = -4(-3) \newline−8x−32y=12 -8x - 32y = 12 \newlineBottom equation after multiplying by 33:\newline3(3x)+3(6y)=3(−4) 3(3x) + 3(6y) = 3(-4) \newline9x+18y=−12 9x + 18y = -12 \newlineNow, add the modified equations:\newline(−8x−32y)+(9x+18y)=12−12 (-8x - 32y) + (9x + 18y) = 12 - 12 \newline−8x+9x−32y+18y=0 -8x + 9x - 32y + 18y = 0 \newlinex−14y=0 x - 14y = 0 \newlineThe y variable is not eliminated.
  4. Determine Strategy B: Determine if strategy B would eliminate a variable without performing the calculations, as we already have two strategies and only need to choose two answers.\newlineStrategy B involves multiplying the top equation by 33 and the bottom equation by 44, then subtracting the bottom equation from the top equation. This would not eliminate a variable because the coefficients of xx and yy would not be opposites.

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