Solve2 is equivalent to Solve, except that it works only for linear equations (and returns just a list) and accepts the options Factoring and FinalSubstitutions.
Solve2 uses the “high school algorithm” and factors intermediate results. Therefore it can be drastically more useful than Solve.
Solve2[{2 x == b - w/2, y - d == p}, {x, y}]\left\{x\to \frac{1}{4} (2 b-w),y\to d+p\right\}
If no equation sign is given the polynomials are supposed to be 0.
Solve2[x + y, x]\{x\to -y\}
Solve2[x + y, x, FinalSubstitutions -> {y -> h}]\{x\to -h\}
Solve2[{2 x == b - w/2, y - d == p}, {x, y}, Factoring -> Expand]\left\{x\to \frac{b}{2}-\frac{w}{4},y\to d+p\right\}
Solve[{2 x == b - w/2, y - d == p}, {x, y}]\left\{\left\{x\to \frac{1}{4} (2 b-w),y\to d+p\right\}\right\}