Linearity of CTFT
F{ax(t) + by(t)} = aX(jw) + bY(jw)
By definition of Fourier Transform:
F{ax(t) + by(t)} = $ \int\limits_{-\infty}^{\infty}(ax(t)+by(t))e^{(-\jmath wt)}dt $
F{ax(t) + by(t)} = $ a\int\limits_{-\infty}^{\infty}x(t)e^{(-\jmath wt)}dt + b\int\limits_{-\infty}^{\infty}y(t)e^{(-\jmath wt)}dt $
F{ax(t) + by(t)} = aX(jw) + bY(jw)
