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Which of these strategies would eliminate a variable in the system of equations? {[10 x+4y=-2],[5x-2y=2]:} Choose 2 answers: A Multiply the top equation by (1)/(2), then add the equations. B Multiply the bottom equation by 2 , then subtract the bottom equation from the top equation. c Add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{10x+4y=−25x−2y=2 \left\{\begin{array}{l} 10 x+4 y=-2 \\ 5 x-2 y=2 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 12 \frac{1}{2} , then add the equations.\newline(B) Multiply the bottom equation by 22 , then subtract the bottom equation from the top equation.\newline(C) Add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{10x+4y=−25x−2y=2 \left\{\begin{array}{l} 10 x+4 y=-2 \\ 5 x-2 y=2 \end{array}\right. \newlineChoose 22 answers:\newline(A) Multiply the top equation by 12 \frac{1}{2} , then add the equations.\newline(B) Multiply the bottom equation by 22 , then subtract the bottom equation from the top equation.\newline(C) Add the equations.
  1. Analyze equations: Analyze the given system of equations to determine which variable can be eliminated using the given strategies.\newlineThe system of equations is:\newline10x+4y=−210x + 4y = -2\newline5x−2y=25x - 2y = 2
  2. Strategy A: Multiply and add: Consider strategy A: Multiply the top equation by (1/2)(1/2), then add the equations.\newlineMultiplying the top equation by (1/2)(1/2) gives us:\newline(1/2)(10x+4y)=(1/2)(−2)(1/2)(10x + 4y) = (1/2)(-2)\newline5x+2y=−15x + 2y = -1\newlineNow, if we add this equation to the bottom equation (5x−2y=2)(5x - 2y = 2), we get:\newline(5x+2y)+(5x−2y)=−1+2(5x + 2y) + (5x - 2y) = -1 + 2\newline10x=110x = 1\newlineThis strategy eliminates the variable 'y'.
  3. Strategy B: Multiply and subtract: Consider strategy B: Multiply the bottom equation by 22, then subtract the bottom equation from the top equation.\newlineMultiplying the bottom equation by 22 gives us:\newline2(5x−2y)=2(2)2(5x - 2y) = 2(2)\newline10x−4y=410x - 4y = 4\newlineNow, if we subtract this equation from the top equation 10x+4y=−210x + 4y = -2, we get:\newline(10x+4y)−(10x−4y)=−2−4(10x + 4y) - (10x - 4y) = -2 - 4\newline8y=−68y = -6\newlineThis strategy eliminates the variable 'x'.
  4. Strategy C: Add equations: Consider strategy C: Add the equations.\newlineIf we add the top equation 10x+4y=−210x + 4y = -2 to the bottom equation 5x−2y=25x - 2y = 2, we get:\newline(10x+4y)+(5x−2y)=−2+2(10x + 4y) + (5x - 2y) = -2 + 2\newline15x+2y=015x + 2y = 0\newlineThis strategy does not eliminate any variable.

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