Which of these strategies would eliminate a variable in the system of equations? {[6x+5y=1],[6x-5y=7]:} Choose 2 answers: A Multiply the top equation by 7 , then subtract the bottom equation from the top equation. B Subtract the bottom equation from the top equation. C. Add the equations.

Question

Which of these strategies would eliminate a variable in the system of equations?  {[6x+5y=1],[6x-5y=7]:} Choose 2 answers: A Multiply the top equation by 7 , then subtract the bottom equation from the top equation. B Subtract the bottom equation from the top equation. C. Add the equations.

Bytelearn · Accepted Answer

Analyze Equations: Analyze the system of equations to determine which strategies could eliminate a variable. We have the system of equations: 6x + 5y = 1 6x - 5y = 7 To eliminate a variable, we can either add or subtract the equations so that one of the variables cancels out.Strategy A: Evaluate Strategy A - Multiply the top equation by 7, then subtract the bottom equation from the top equation. If we multiply the top equation by 7, we get: (6x + 5y) * 7 = 1 * 7 42x + 35y = 7 Now, if we subtract the bottom equation from this new equation: (42x + 35y) - (6x - 5y) = 7 - 7 This would result in: 42x + 35y - 6x + 5y = 0 36x + 40y = 0 This does not eliminate any variable.Strategy B: Evaluate Strategy B - Subtract the bottom equation from the top equation. If we subtract the bottom equation from the top equation, we get: (6x + 5y) - (6x - 5y) = 1 - 7 This simplifies to: 6x + 5y - 6x + 5y = -6 10y = -6 This strategy eliminates the variable x.Strategy C: Evaluate Strategy C - Add the equations. If we add the two equations, we get: (6x + 5y) + (6x - 5y) = 1 + 7 This simplifies to: 12x = 8 This strategy eliminates the variable y.

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