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Determine the standard form of the following equation:\newliney=8x7y = 8x - 7

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Q. Determine the standard form of the following equation:\newliney=8x7y = 8x - 7
  1. Identify Equation: Identify the given equation and the standard form requirement.\newlineThe given equation is y=8x7y = 8x - 7, and we need to rewrite it in the standard form Ax+By=CAx + By = C, where AA, BB, and CC are integers with a greatest common factor (GCF) of 11, and AA should be non-negative.
  2. Move Term for Isolation: Move the term involving xx to the other side of the equation to isolate yy. To do this, we subtract 8x8x from both sides of the equation. y=8x7y = 8x - 7 y8x=7y - 8x = -7
  3. Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=CAx + By = C. We want the xx term to come before the yy term, so we write the equation as: 8x+y=7-8x + y = -7
  4. Ensure Non-Negative Coefficient: Ensure that the coefficient of xx is non-negative.\newlineIf the coefficient of xx is negative, we can multiply the entire equation by 1-1 to make it positive.\newline1(8x+y)=1(7)-1(-8x + y) = -1(-7)\newline8xy=78x - y = 7
  5. Check for GCF: Check if the coefficients have a GCF other than 11. The coefficients are 88, 1-1, and 77. The GCF of these numbers is 11, so we do not need to divide the entire equation by any number.

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