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Solve the equation 273 + y − 3x = 0 for y in terms of x.

Mathematics

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Answer

y=3x−19683y = 3x - 19683

Step-by-step solution

3 steps

The given equation is 273+y−3x=027^3 + y - 3x = 0. This is a linear equation with two variables, xx and yy. To "solve" it means to express one variable in terms of the other.

  1. Calculate the value of the constant term 27327^3.

    273=1968327^3 = 19683
  2. Substitute the calculated value back into the equation.

    19683+y−3x=019683 + y - 3x = 0
  3. Rearrange the equation to express yy in terms of xx.

    Add 3x3x to both sides and subtract 19683 from both sides:

    y=3x−19683y = 3x - 19683

    Alternatively, you could express xx in terms of yy:

    3x=y+196833x = y + 19683 x=13y+196833x = \frac{1}{3}y + \frac{19683}{3} x=13y+6561x = \frac{1}{3}y + 6561

    Since there is only one equation with two variables, there are infinitely many solutions, and the solution is expressed as a relationship between xx and yy.

    We will provide the solution for yy in terms of xx.

    y=3x−19683\boxed{y = 3x - 19683}

    One more to go today! Send it over.

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