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Rewrite the following equation in standard form.\newliney=10x+5y = 10x + 5\newlineHint: The standard form of a linear equation is Ax+By=CAx + By = C where AA and BB are not both zero, and AA, BB, and CC are integers whose GCF is 11.

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Q. Rewrite the following equation in standard form.\newliney=10x+5y = 10x + 5\newlineHint: The standard form of a linear equation is Ax+By=CAx + By = C where AA and BB are not both zero, and AA, BB, and CC are integers whose GCF is 11.
  1. Identify Equation & Requirement: Identify the given equation and the standard form requirement.\newlineThe given equation is y=10x5y = 10x - 5, 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 Involving xx: Move the term involving xx to the other side of the equation to isolate the constant term.\newlineTo do this, we subtract 10x10x from both sides of the equation.\newliney10x=5y - 10x = -5\newlineHowever, this is not the standard form yet because the xx term should be on the left side of the equation.
  3. Rearrange Terms: Rearrange the terms to place the xx term on the left side and the constant on the right side.\newlineWe rewrite the equation from Step 22 as:\newline10x+y=5-10x + y = -5
  4. Ensure Positive Coefficient: Ensure that the coefficient of xx is positive. Since the standard form requires the coefficient of xx to be positive, we multiply the entire equation by 1-1 to get: 10xy=510x - y = 5 Now the equation is in standard form with A=10A = 10, B=1B = -1, and C=5C = 5.

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