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Rewrite the following equation in standard form.\newliney=2x+3y = 2x + 3\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+3y = 2x + 3\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 for standard form: To convert the equation y=2x+3y = 2x + 3 into standard form, we need to rearrange the terms so that the xx and yy terms are on one side of the equation and the constant is on the other side. We want it in the form Ax+By=CAx + By = C.
  2. Subtract 2x2x: Subtract 2x2x from both sides of the equation to move the xx term to the left side of the equation. This gives us:\newliney2x=32xy - 2x = 3 - 2x
  3. Simplify the equation: Simplify the equation by combining like terms. Since there are no like terms on the right side, we just rewrite the equation as: \newline2x+y=3-2x + y = 3
  4. Make A positive: The standard form of a linear equation is Ax+By=CAx + By = C, where AA is a positive integer. Since 2-2 is negative, we multiply the entire equation by 1-1 to make AA positive:\newline1(2x+y)=1(3)-1(-2x + y) = -1(3)
  5. Distribute 1-1: Distribute the 1-1 across each term in the equation: 2xy=32x - y = -3
  6. Final standard form: The equation 2xy=32x - y = -3 is now in standard form, with A=2A = 2, B=1B = -1, and C=3C = -3. The greatest common factor (GCF) of AA, BB, and CC is 11, which satisfies the conditions for standard form.

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