Clear[x, y, z, w];
eq1 = -0.7*w + 0.3*y + 0.4*z == 0;
eq2 = -0.6*x + 0.2*y + 0.1*z == 0;
eq3 = 0.5*w + 0.3*x - y == 0;
eq4 = 0.2*w + 0.3*x + 0.5*y - 0.5*z == 0;
eq5 = w + x + y + z == 1;
Solve[{eq1, eq2, eq3, eq4, eq5}, {z, w, x, y}]