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Rewrite the following equation in standard form.\newliney=2x+9y = 2x + 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=2x+9y = 2x + 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. Rearrange terms to standard form: Now we need to rearrange the terms to match the standard form Ax+By=CAx + By = C.\newlineWe write the xx term first, followed by the yy term.\newline2x+y=9-2x + y = -9
  2. Make coefficient of x positive: However, the standard form typically has a positive AA coefficient. To ensure this, we can multiply the entire equation by 1-1 to make the coefficient of xx positive.\newlineMultiplying both sides by 1-1 gives us:\newline2xy=92x - y = 9
  3. Check coefficients for GCF: Finally, we check that the coefficients AA, BB, and CC are integers whose greatest common factor (GCF) is 11. The coefficients are 22, 1-1, and 99. The GCF of these numbers is indeed 11.

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