Given nonzero numbers x0, y0, u0, v0, s0, t0 which satisfy the simultaneous equations

prove that there exist functions u(x, y), v(x, y), s(x, y), t(x, y), and an open ball containing (x0, y0), such that u, v, s, t are continuously differentiable and satisfy (*) on B, and such that u(x0, y0) = uo, v(x0, y0) = v0, s(x0, y0) = s0, and t(x0, y0) = t0.

C) 112 + sx + ty =0 2s2x + 212y-1 = 0