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Rewrite the following equation in standard form.\newliney=5x+4y = 5x + 4\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=5x+4y = 5x + 4\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=5x+4y = 5x + 4, and 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. Move Term for Isolation: Move the term involving xx to the other side of the equation to isolate yy. To do this, we subtract 5x5x from both sides of the equation. y5x=45xy - 5x = 4 - 5x This results in 5x+y=4-5x + y = 4, which is almost in standard form, but we typically want the xx-term to be positive.
  3. Make Coefficient Positive: Multiply the entire equation by 1-1 to make the coefficient of xx positive.\newlineMultiplying by 1-1, we get:\newline1(5x+y)=1(4)-1(-5x + y) = -1(4)\newline5xy=45x - y = -4\newlineNow, we have the xx-term positive, but the yy-term is negative.
  4. Rearrange for Standard Form: Rearrange the terms to match the standard form Ax+By=CAx + By = C. We want the equation to be in the form of Ax+By=CAx + By = C, so we move the y-term to the other side by adding yy to both sides. 5xy+y=4+y5x - y + y = -4 + y This simplifies to: 5x+0y=4+y5x + 0y = -4 + y Which is the same as: 5x=y45x = y - 4 However, we need to have both xx and yy on the same side, so we add yy to both sides to get the final standard form. 5x+y=45x + y = 4

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