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Rewrite the following equation in standard form.\newliney=9x+5y = 9x + 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=9x+5y = 9x + 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: Identify the given equation and the standard form requirement.\newlineThe given equation is y=9x+5y = 9x + 5. 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. Rearrange Terms: Rearrange the equation to get terms involving xx and yy on one side and the constant on the other side.\newlineTo do this, we will subtract 9x9x from both sides of the equation to move the term involving xx to the left side.\newliney9x=59xy - 9x = 5 - 9x\newlineThis simplifies to:\newline9x+y=5-9x + y = 5
  3. Ensure Non-Negative Coefficient: Ensure that the coefficient of xx is non-negative.\newlineThe standard form prefers the coefficient of xx to be positive. To achieve this, we can multiply the entire equation by 1-1.\newline1(9x+y)=1(5)-1(-9x + y) = -1(5)\newlineThis simplifies to:\newline9xy=59x - y = -5
  4. Check GCF of Coefficients: Check if the coefficients have a GCF other than 11. The coefficients are 99, 1-1, and 5-5. The GCF of these numbers is 11.
  5. Write Final Equation: Write the final equation in standard form.\newlineThe equation in standard form is:\newline9xy=59x - y = -5

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