5. Given nonzero numbers xo, Yo, un, va, So, to that satisfy the simultaneous equations

(*) u2 + sx + ty = 0 v2 + tx + sy = 0 2s2x + 2t2y - 1 = 0 S2X - t2y = 0, prove that there exist functions u(x, y), v(x, y), s(x, y), t(x, y), and an open ball B containing (xo, Yo), such that u, v, s, t are continuously differentiable and satisfy (*) on B, and such that u(xo, Yo) = un, v(xo, Yo) = va, s(xo, Yo) = So, and t(xo, Yo) = to·