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Which of these strategies would eliminate a variable in the system of equations? {[-x+6y=8],[7x-y=-2]:} Choose 1 answers: A Add the equations. B Multiply the bottom equation by 6 , then subtract the bottom equation from the top equation. c Multiply the top equation by 7 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{−x+6y=87x−y=−2 \left\{\begin{array}{l} -x+6 y=8 \\ 7 x-y=-2 \end{array}\right. \newlineChoose 11 answers:\newline(A) Add the equations.\newline(B) Multiply the bottom equation by 66 , then subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by 77 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{−x+6y=87x−y=−2 \left\{\begin{array}{l} -x+6 y=8 \\ 7 x-y=-2 \end{array}\right. \newlineChoose 11 answers:\newline(A) Add the equations.\newline(B) Multiply the bottom equation by 66 , then subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by 77 , then add the equations.
  1. Analyze the system: Analyze the given system of equations to determine which strategy would eliminate a variable.\newlineThe system of equations is:\newline−x+6y=8-x + 6y = 8\newline7x−y=−27x - y = -2\newlineWe need to find a strategy that will eliminate either ′x′'x' or ′y′'y' when we combine the two equations.
  2. Evaluate option A: Evaluate option A: Add the equations.\newlineIf we add the equations directly, we get:\newline(−x+6y)+(7x−y)=8+(−2)(-x + 6y) + (7x - y) = 8 + (-2)\newlineThis simplifies to:\newline6x+5y=66x + 5y = 6\newlineThis does not eliminate any variable.
  3. Evaluate option B: Evaluate option B: Multiply the bottom equation by 66, then subtract the bottom equation from the top equation.\newlineFirst, we multiply the bottom equation by 66:\newline6×(7x−y)=6×(−2)6 \times (7x - y) = 6 \times (-2)\newlineThis gives us:\newline42x−6y=−1242x - 6y = -12\newlineNow, we subtract this new equation from the top equation:\newline(−x+6y)−(42x−6y)=8−(−12)(-x + 6y) - (42x - 6y) = 8 - (-12)\newlineThis simplifies to:\newline−x+6y−42x+6y=8+12-x + 6y - 42x + 6y = 8 + 12\newlineCombining like terms, we get:\newline−43x+12y=20-43x + 12y = 20\newlineThis does not eliminate any variable.
  4. Evaluate option C: Evaluate option C: Multiply the top equation by 77, then add the equations.\newlineFirst, we multiply the top equation by 77:\newline7⋅(−x+6y)=7⋅87 \cdot (-x + 6y) = 7 \cdot 8\newlineThis gives us:\newline−7x+42y=56-7x + 42y = 56\newlineNow, we add this new equation to the bottom equation:\newline(−7x+42y)+(7x−y)=56+(−2)(-7x + 42y) + (7x - y) = 56 + (-2)\newlineThis simplifies to:\newline−7x+42y+7x−y=54-7x + 42y + 7x - y = 54\newlineCombining like terms, we get:\newline41y=5441y = 54\newlineThis eliminates the variable 'x'.

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