Write the following in general form:

Y=3x-7
Y=3+x/4
5x=2y-1

1 answer

To write the given equations in general form, we need to rearrange each equation into the form \(Ax + By + C = 0\), where \(A\), \(B\), and \(C\) are integers.

  1. Equation 1: \(Y = 3x - 7\)

    Rearranging: \[ 3x - Y - 7 = 0 \] General Form: \[ 3x - Y - 7 = 0 \quad \text{or} \quad 3x - Y = 7 \]

  2. Equation 2: \(Y = 3 + \frac{x}{4}\)

    Rearranging: \[ Y - \frac{x}{4} - 3 = 0 \] To eliminate the fraction, multiply by 4: \[ 4Y - x - 12 = 0 \] General Form: \[ -x + 4Y - 12 = 0 \quad \text{or} \quad x - 4Y + 12 = 0 \]

  3. Equation 3: \(5x = 2y - 1\)

    Rearranging: \[ 5x - 2y + 1 = 0 \] General Form: \[ 5x - 2y + 1 = 0 \]

Putting all equations together, we get:

  1. \(3x - Y - 7 = 0\) (or \(3x - Y = 7\))
  2. \(x - 4Y + 12 = 0\)
  3. \(5x - 2y + 1 = 0\)