Which of these strategies would eliminate a variable in the system of equations? {[2x+8y=-3],[3x+6y=-4]:} Choose 2 answers: A Multiply the top equation by 3 , multiply the bottom equation by -2 , then add the equations. B Multiply the top equation by 3 , multiply the bottom equation by 4 , then subtract the bottom equation from the top equation. C Multiply the top equation by -4 , multiply the bottom equation by 3 , then add the equations.

Question

Which of these strategies would eliminate a variable in the system of equations?  {[2x+8y=-3],[3x+6y=-4]:} Choose 2 answers: A Multiply the top equation by 3 , multiply the bottom equation by -2 , then add the equations. B Multiply the top equation by 3 , multiply the bottom equation by 4 , then subtract the bottom equation from the top equation. C Multiply the top equation by -4 , multiply the bottom equation by 3 , then add the equations.

Bytelearn · Accepted Answer

Analyze System of Equations: Analyze the given system of equations to determine how to eliminate a variable. The system of equations is: $$ \begin{cases}  2x + 8y = -3 \ 3x + 6y = -4  \end{cases} $$ To eliminate a variable, we need to make the coefficients of either x or y in both equations the same with opposite signs so that when we add or subtract the equations, one of the variables cancels out.Apply Strategy A: Apply strategy A to see if it eliminates a variable. Strategy A suggests: Multiply the top equation by 3 and the bottom equation by -2. The equations become: $$ \begin{cases}  (2x + 8y) \cdot 3 = -3 \cdot 3 \ (3x + 6y) \cdot -2 = -4 \cdot -2  \end{cases} $$ Which simplifies to: $$ \begin{cases}  6x + 24y = -9 \ -6x - 12y = 8  \end{cases} $$ Now, add the equations: $$ (6x + 24y) + (-6x - 12y) = -9 + 8 $$ $$ 6x - 6x + 24y - 12y = -1 $$ $$ 0x + 12y = -1 $$ The x variable is eliminated.Apply Strategy B: Apply strategy B to see if it eliminates a variable. Strategy B suggests: Multiply the top equation by 3 and the bottom equation by 4, then subtract the bottom equation from the top equation. The equations become: $$ \begin{cases}  (2x + 8y) \cdot 3 = -3 \cdot 3 \ (3x + 6y) \cdot 4 = -4 \cdot 4  \end{cases} $$ Which simplifies to: $$ \begin{cases}  6x + 24y = -9 \ 12x + 24y = -16  \end{cases} $$ Now, subtract the bottom equation from the top equation: $$ (6x + 24y) - (12x + 24y) = -9 - (-16) $$ $$ 6x - 12x + 24y - 24y = -9 + 16 $$ $$ -6x + 0y = 7 $$ The y variable is eliminated.Apply Strategy C: Apply strategy C to see if it eliminates a variable. Strategy C suggests: Multiply the top equation by -4 and the bottom equation by 3. The equations become: $$ \begin{cases}  (2x + 8y) \cdot -4 = -3 \cdot -4 \ (3x + 6y) \cdot 3 = -4 \cdot 3  \end{cases} $$ Which simplifies to: $$ \begin{cases}  -8x - 32y = 12 \ 9x + 18y = -12  \end{cases} $$ Now, add the equations: $$ (-8x - 32y) + (9x + 18y) = 12 + (-12) $$ $$ -8x + 9x - 32y + 18y = 0 $$ $$ x - 14y = 0 $$ The x variable is not eliminated, and neither is the y variable.

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