Solve3 is equivalent to Solve, except that it works only for linear equations (and returns just a list) and uses the “high school algorithm.
Sometimes it is better than Solve for systems involving rational polynomials.
Solve3[{2 x == b - w/2, y - d == p}, {x, y}]\left\{x\to \frac{1}{4} (2 b-w),y\to d+p\right\}