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Which of these strategies would eliminate a variable in the system of equations? {[8x+5y=-7],[-7x+6y=-4]:} Choose 1 answers: A Multiply the top equation by 6 , multiply the bottom equation by -5 , then add the equations. B Multiply the top equation by 7 , then add the equations. C Multiply the bottom equation by 8 , then add the equations.

Which of these strategies would eliminate a variable in the system of equations?\newline{8x+5y=−7−7x+6y=−4 \left\{\begin{array}{l} 8 x+5 y=-7 \\ -7 x+6 y=-4 \end{array}\right. \newlineChoose 11 answers:\newline(A) Multiply the top equation by 66 , multiply the bottom equation by −5-5 , then add the equations.\newline(B) Multiply the top equation by 77 , then add the equations.\newline(C) Multiply the bottom equation by 88 , then add the equations.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{8x+5y=−7−7x+6y=−4 \left\{\begin{array}{l} 8 x+5 y=-7 \\ -7 x+6 y=-4 \end{array}\right. \newlineChoose 11 answers:\newline(A) Multiply the top equation by 66 , multiply the bottom equation by −5-5 , then add the equations.\newline(B) Multiply the top equation by 77 , then add the equations.\newline(C) Multiply the bottom equation by 88 , then add the equations.
  1. Analyze strategies: Analyze the given strategies to determine which one will eliminate a variable.\newlineWe have the system of equations:\newline8x+5y=−78x + 5y = -7\newline−7x+6y=−4-7x + 6y = -4\newlineWe need to find a strategy that will result in the coefficients of either xx or yy being opposites so that when we add the equations, one of the variables will be eliminated.
  2. Evaluate option A: Evaluate option A.\newlineOption A suggests multiplying the top equation by 66 and the bottom equation by −5-5, then adding the equations.\newlineLet's perform the multiplication to see if it will eliminate a variable:\newline(8x+5y)×6=48x+30y(8x + 5y) \times 6 = 48x + 30y\newline(−7x+6y)×−5=35x−30y(-7x + 6y) \times -5 = 35x - 30y\newlineNow, let's add the equations to see if a variable is eliminated:\newline48x+30y+35x−30y=0x+0y48x + 30y + 35x - 30y = 0x + 0y, which simplifies to 83x=083x = 0\newlineThis does not eliminate a variable.
  3. Evaluate option B: Evaluate option B.\newlineOption B suggests multiplying the top equation by 77, then adding the equations.\newlineLet's perform the multiplication to see if it will eliminate a variable:\newline(8x+5y)×7=56x+35y(8x + 5y) \times 7 = 56x + 35y\newlineNow, let's add the equations to see if a variable is eliminated:\newline56x+35y+(−7x+6y)=49x+41y56x + 35y + (-7x + 6y) = 49x + 41y\newlineThis does not eliminate a variable.
  4. Evaluate option C: Evaluate option C.\newlineOption C suggests multiplying the bottom equation by 88, then adding the equations.\newlineLet's perform the multiplication to see if it will eliminate a variable:\newline(−7x+6y)×8=−56x+48y(-7x + 6y) \times 8 = -56x + 48y\newlineNow, let's add the equations to see if a variable is eliminated:\newline8x+5y+(−56x+48y)=−48x+53y8x + 5y + (-56x + 48y) = -48x + 53y\newlineThis does not eliminate a variable.
  5. Determine correct strategy: Determine the correct strategy.\newlineUpon evaluating all options, we see that option A is the correct strategy because it results in the yy terms being opposites (30y30y and −30y-30y), which will eliminate the yy variable when the equations are added together.

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