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Which of these strategies would eliminate a variable in the system of equations? {[8x+8y=2],[8x+5y=1]:} Choose 1 answers: Add the equations. Subtract the bottom equation from the top equation. Multiply the top equation by (1)/(2), then subtract the bottom equation from the top equation.

Which of these strategies would eliminate a variable in the system of equations?\newline{8x+8y=28x+5y=1 \left\{\begin{array}{l} 8 x+8 y=2 \\ 8 x+5 y=1 \end{array}\right. \newlineChoose 11 answers:\newline(A) Add the equations.\newline(B) Subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by 12 \frac{1}{2} , then subtract the bottom equation from the top equation.

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Q. Which of these strategies would eliminate a variable in the system of equations?\newline{8x+8y=28x+5y=1 \left\{\begin{array}{l} 8 x+8 y=2 \\ 8 x+5 y=1 \end{array}\right. \newlineChoose 11 answers:\newline(A) Add the equations.\newline(B) Subtract the bottom equation from the top equation.\newline(C) Multiply the top equation by 12 \frac{1}{2} , then subtract the bottom equation from the top equation.
  1. Analyze the system: Analyze the system of equations to determine which strategy would eliminate a variable.\newlineWe have the system of equations:\newline8x+8y=28x + 8y = 2\newline8x+5y=18x + 5y = 1\newlineTo eliminate a variable, we need to make the coefficients of that variable the same with opposite signs or identical so that they cancel each other out when we add or subtract the equations.
  2. Evaluate first strategy: Evaluate the given strategies to see which one will eliminate a variable.\newlineThe first strategy is to add the equations. If we add them as they are, we get:\newline(8x+8y)+(8x+5y)=2+1(8x + 8y) + (8x + 5y) = 2 + 1\newline16x+13y=316x + 13y = 3\newlineThis does not eliminate any variable.
  3. Evaluate second strategy: Evaluate the second strategy, which is to subtract the bottom equation from the top equation.\newline(8x+8y)−(8x+5y)=2−1(8x + 8y) - (8x + 5y) = 2 - 1\newline8x+8y−8x−5y=18x + 8y - 8x - 5y = 1\newlineThe 8x8x terms cancel out, leaving us with:\newline3y=13y = 1\newlineThis strategy eliminates the variable xx.
  4. Evaluate third strategy: Evaluate the third strategy, which is to multiply the top equation by (1)/(2)(1)/(2), then subtract the bottom equation from the top equation.\newlineFirst, we multiply the top equation by (1)/(2)(1)/(2):\newline(1/2)×(8x+8y)=(1/2)×2(1/2) \times (8x + 8y) = (1/2) \times 2\newline4x+4y=14x + 4y = 1\newlineNow we subtract the bottom equation from this new equation:\newline(4x+4y)−(8x+5y)=1−1(4x + 4y) - (8x + 5y) = 1 - 1\newline4x+4y−8x−5y=04x + 4y - 8x - 5y = 0\newline−4x−y=0-4x - y = 0\newlineThis strategy does not eliminate a variable immediately, and it also results in a math error because the subtraction was not performed correctly.

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