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Rewrite the following equation in standard form.\newliney=2x+10y = 2x + 10\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=2x+10y = 2x + 10\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: Identify the given equation and the standard form requirement.\newlineThe given equation is y=2x+10y = 2x + 10. 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: Move the term involving xx to the other side of the equation to isolate the constant term on one side.\newlineTo do this, we subtract 2x2x from both sides of the equation.\newliney2x=2x+102xy - 2x = 2x + 10 - 2x\newlineThis simplifies to:\newliney2x=10y - 2x = 10
  3. Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=CAx + By = C. We want the xx term first, followed by the yy term, equaling the constant. 2x+y=10-2x + y = 10
  4. Ensure Non-Negative Coefficient: Ensure that the coefficient of xx is non-negative.\newlineIf we multiply the entire equation by 1-1, we will get the coefficient of xx to be positive, which is a common convention for standard form.\newline(1)(2x)+(1)y=(1)10(-1)(-2x) + (-1)y = (-1)10\newlineThis simplifies to:\newline2xy=102x - y = -10
  5. Check GCF: Check if the coefficients have a GCF other than 11. The coefficients are 22, 1-1, and 10-10. The GCF of these numbers is 11.

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