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Rewrite the following equation in standard form.\newliney=7x+7y = 7x + 7\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=7x+7y = 7x + 7\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. Start Equation Rewrite Standard Form: Start with the given equation.\newlineThe given equation is y=7x7y = 7x - 7. We need to rewrite it in standard form, which is Ax+By=CAx + By = C.
  2. Move Term with x: Move the term with x to the other side of the equation.\newlineTo do this, we subtract 7x7x from both sides of the equation to get 7x+y=7-7x + y = -7.
  3. Check Coefficients Common Factors: Check the coefficients for any common factors.\newlineThe coefficients of the terms in the equation 7x+y=7-7x + y = -7 are 7-7, 11, and 7-7. The greatest common factor (GCF) of these numbers is 11, so we do not need to divide any terms to reduce the coefficients.
  4. Ensure Positive Coefficient xx: Ensure that the coefficient of xx is positive.\newlineThe standard form prefers the coefficient of xx to be positive. To achieve this, we can multiply the entire equation by 1-1 to get 7xy=77x - y = 7.
  5. Write Final Equation: Write the final equation in standard form.\newlineThe final equation in standard form is 7xy=77x - y = 7.

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