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Which of these strategies would eliminate a variable in the system of equations? {[2x+3y=-5],[2x-3y=10]:} Choose 2 answers: A Subtract the bottom equation from the top equation. B Add the equations. c Multiply the top equation by 2 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{2x+3y=−52x−3y=10 \left\{\begin{array}{l} 2 x+3 y=-5 \\ 2 x-3 y=10 \end{array}\right. \newlineChoose 22 answers:\newline(A) Subtract the bottom equation from the top equation.\newline(B) Add the equations.\newline(C) Multiply the top equation by 22 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{2x+3y=−52x−3y=10 \left\{\begin{array}{l} 2 x+3 y=-5 \\ 2 x-3 y=10 \end{array}\right. \newlineChoose 22 answers:\newline(A) Subtract the bottom equation from the top equation.\newline(B) Add the equations.\newline(C) Multiply the top equation by 22 , then add the equations.
  1. Analyze the system: Analyze the given system of equations to determine which strategies could eliminate a variable.\newlineThe system of equations is:\newline2x+3y=−52x + 3y = -5\newline2x−3y=102x - 3y = 10\newlineWe need to find out if subtracting one equation from the other or adding them together would eliminate one of the variables.
  2. Subtracting equations: Consider option A, which suggests subtracting the bottom equation from the top equation.\newlinePerform the subtraction: (2x+3y)−(2x−3y)=−5−10(2x + 3y) - (2x - 3y) = -5 - 10\newlineThis simplifies to: 2x+3y−2x+3y=−152x + 3y - 2x + 3y = -15\newlineWhich further simplifies to: 6y=−156y = -15\newlineThis strategy eliminates the variable xx.
  3. Adding equations: Consider option B, which suggests adding the equations.\newlinePerform the addition: (2x+3y)+(2x−3y)=−5+10(2x + 3y) + (2x - 3y) = -5 + 10\newlineThis simplifies to: 2x+3y+2x−3y=52x + 3y + 2x - 3y = 5\newlineWhich further simplifies to: 4x=54x = 5\newlineThis strategy also eliminates the variable 'y'.
  4. Multiplying and adding equations: Consider option C, which suggests multiplying the top equation by 22, then adding the equations.\newlineFirst, multiply the top equation by 22: 2(2x+3y)=2(−5)2(2x + 3y) = 2(-5)\newlineThis simplifies to: 4x+6y=−104x + 6y = -10\newlineNow, add this result to the bottom equation: (4x+6y)+(2x−3y)=−10+10(4x + 6y) + (2x - 3y) = -10 + 10\newlineThis simplifies to: 6x+3y=06x + 3y = 0\newlineThis strategy does not eliminate any variable, as we end up with a new equation with both variables still present.

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