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

Which of these strategies would eliminate a variable in the system of equations?\newline{2x−6y=66x−4y=2 \left\{\begin{array}{l} 2 x-6 y=6 \\ 6 x-4 y=2 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by −3-3 , then add the equations.\newline(B) Multiply the bottom equation by 33 , then subtract the bottom equation from the top equation.\newline(C) Multiply the bottom equation by −32 -\frac{3}{2} , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{2x−6y=66x−4y=2 \left\{\begin{array}{l} 2 x-6 y=6 \\ 6 x-4 y=2 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by −3-3 , then add the equations.\newline(B) Multiply the bottom equation by 33 , then subtract the bottom equation from the top equation.\newline(C) Multiply the bottom equation by −32 -\frac{3}{2} , then add the equations.
  1. Step 11: Analyze the system of equations: Analyze the given system of equations to determine which variable can be eliminated using the proposed strategies.\newlineThe system of equations is:\newline2x−6y=62x - 6y = 6\newline6x−4y=26x - 4y = 2
  2. Step 22: Evaluate strategy A: Evaluate strategy A: Multiply the top equation by −3-3, then add the equations.\newlineMultiplying the top equation by −3-3 gives us:\newline−3(2x−6y)=−3(6)-3(2x - 6y) = -3(6)\newline−6x+18y=−18-6x + 18y = -18\newlineNow, we add this to the bottom equation:\newline(−6x+18y)+(6x−4y)=(−18+2)(-6x + 18y) + (6x - 4y) = (-18 + 2)\newlineThe xx terms cancel out, and we are left with:\newline14y=−1614y = -16\newlineThis strategy successfully eliminates the variable xx.
  3. Step 33: Evaluate strategy B: Evaluate strategy B: Multiply the bottom equation by 33, then subtract the bottom equation from the top equation.\newlineMultiplying the bottom equation by 33 gives us:\newline3(6x−4y)=3(2)3(6x - 4y) = 3(2)\newline18x−12y=618x - 12y = 6\newlineNow, we subtract this from the top equation:\newline(2x−6y)−(18x−12y)=(6−6)(2x - 6y) - (18x - 12y) = (6 - 6)\newlineThe y terms do not cancel out, and we are left with:\newline−16x+6y=0-16x + 6y = 0\newlineThis strategy does not eliminate any variable.
  4. Step 44: Evaluate strategy C: Evaluate strategy C: Multiply the bottom equation by −32-\frac{3}{2}, then add the equations.\newlineMultiplying the bottom equation by −32-\frac{3}{2} gives us:\newline−32(6x−4y)=−32(2)-\frac{3}{2}(6x - 4y) = -\frac{3}{2}(2)\newline−9x+6y=−3-9x + 6y = -3\newlineNow, we add this to the top equation:\newline(2x−6y)+(−9x+6y)=(6−3)(2x - 6y) + (-9x + 6y) = (6 - 3)\newlineThe yy terms cancel out, and we are left with:\newline−7x=3-7x = 3\newlineThis strategy successfully eliminates the variable yy.

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