3x + b = 5x - 7 3y + c = 5y - 7In the equations above, b and c are constants. ...

Choice A is correct. Subtracting the sides of 3y + c = 5y - 7 from the corresponding sides of 3x + b = 5x - 7 gives (3x - 3y) + (b - c) = (5x - 5y) + (-7 - (-7)). Since b = c - \(\frac{1}{2}\), or b - c = -\(\frac{1}{2}\),  it follows that (3x - 3y) + (-\(\frac{1}{2}\)) = (5x - 5y). Solving this equation for x in terms of y gives x = y - \(\frac{1}{4}\). Therefore, x is y minus \(\frac{1}{4}\).

Choices B, C, and D are incorrect and may be the result of making a computational error when solving the equations for x in terms of y.