NDSolve

ClearAll["Global`*"]
a = 35;
b = 3;
c = 28;
s = NDSolve[{a (y[t] - x[t]) ==
    x'[t], (c - a) x[t] - x[t] z[t] + c*y[t] == y'[t],
   x[t] y[t] - b*z[t] == z'[t], x[0] == -10, y[0] == 0,
   z[0] == 37}, {x, y, z}, {t, 0, 7}]
Plot[Evaluate[{x[t], y[t], z[t]} /. s], {t, 0, 7},
 PlotStyle -> Automatic]