{{x1, y1}, {x2, y2}} = Solve[y^2 == 13 x + 17 && y == 193 x + 29, {x, y}][[All, All, -1]] (* {{(-11181 - Sqrt[2242057])/74498, 1/386 (13 - Sqrt[2242057])}, {(-11181 + Sqrt[2242057])/74498, 1/386 (13 + Sqrt[2242057])}} *) {x1, y2} (* {(-11181- Sqrt[2242057]) / 74498, 1 / 386 (13 + Sqrt[2242057])} *) 

Update: Version 10 built-in function Values does value extraction conveniently for rules appearing in lists of arbitrary lengths and depths:

{{x1, y1}, {x2, y2}} = Values[Solve[y^2 == 13 x + 17 && y == 193 x + 29, {x, y}]] (* {{(-11181-Sqrt[2242057])/74498,1/386 (13-Sqrt[2242057])}, {(-11181+Sqrt[2242057])/74498,1/386 (13+Sqrt[2242057])}} *) 

Another example:

lst={{a->1,b->2},{c->3},{{d->4}},{e->5,{f->6,{g->7}}}}; Values[lst] (* {{1,2},{3},{{4}},{5,{6,{7}}}} *) 

Original post:

{{x1, y1}, {x2, y2}} = Solve[y^2 == 13 x + 17 && y == 193 x + 29, {x, y}][[All, All, -1]] (* {{(-11181 - Sqrt[2242057])/74498, 1/386 (13 - Sqrt[2242057])}, {(-11181 + Sqrt[2242057])/74498, 1/386 (13 + Sqrt[2242057])}} *) {x1, y2} (* {(-11181- Sqrt[2242057]) / 74498, 1 / 386 (13 + Sqrt[2242057])} *)