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Rewrite the following equation in standard form.\newliney=4x+3y = 4x + 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=4x+3y = 4x + 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. Identify Equation: Identify the given equation and the standard form requirement.\newlineThe given equation is y=4x3y = 4x - 3, and we need to rewrite it in the standard form Ax+By=CAx + By = C.
  2. Move Term for Isolation: Move the term with xx to the other side of the equation to isolate the constant term.\newlineTo do this, we subtract 4x4x from both sides of the equation.\newliney4x=3y - 4x = -3
  3. Rearrange Equation: Rearrange the equation so that the xx term comes before the yy term.4x+y=3-4x + y = -3
  4. Check Coefficients: Check if the coefficients are integers and their greatest common factor (GCF) is 11. The coefficients are 4-4, 11, and 3-3. Their GCF is 11.
  5. Ensure Positive Coefficient: Ensure that the coefficient of xx is positive.\newlineIf we want the coefficient of xx to be positive, we can multiply the entire equation by 1-1.\newline4xy=34x - y = 3

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