DSolve[{Derivative[1][x][t] == -3*x[t] + 48*y[t] - 28*z[t], Derivative[1][y][t] == -4*x[t] + 40*y[t] - 22*z[t], Derivative[1][z][t] == -6*x[t] + 57*y[t] - 31*z[t]},{x[t], y[t], z[t]},t]