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Rewrite the following equation in standard form.\newliney=6x+9y = 6x + 9\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.

Full solution

Q. Rewrite the following equation in standard form.\newliney=6x+9y = 6x + 9\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. Given Equation: Start with the given equation.\newliney=6x+9y = 6x + 9\newlineWe need to rearrange this equation into the standard form, which is Ax+By=CAx + By = C.
  2. Rearrange Equation: Move the term involving xx to the other side of the equation by subtracting 6x6x from both sides.\newliney6x=6x+96xy - 6x = 6x + 9 - 6x\newlineThis simplifies to:\newliney6x=9y - 6x = 9
  3. Rewrite Equation: To write the equation in standard form, we need to have the xx-term first. So, we rewrite the equation as: 6x+y=9-6x + y = 9
  4. Make Coefficient Positive: The standard form of a linear equation should have a positive coefficient for xx if possible. To achieve this, we can multiply the entire equation by 1-1 to make the coefficient of xx positive.\newline1(6x+y)=1(9)-1(-6x + y) = -1(9)\newlineThis simplifies to:\newline6xy=96x - y = -9
  5. Check for GCF: Check if the coefficients have a greatest common factor (GCF) other than 11. The coefficients are 66, 1-1, and 9-9. The GCF of these numbers is 11.

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