Just as there are simultaneous algebraic equations $($where a pair of numbers have to sutisfy a pair of equations$)$ there are oyerms of differential equation functions have to satisfy a pair of differential equations$).$

Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations.

$y_1^{\text{'}}=y_1-2y_2,y_1=3y_1-4y_2$

A$.y_1=2e^{-2x},y_2=3e^{-2x}$

B$.y_1=e^{4r},y_2=e^{4r}$

C$.{?}_{y_1}=cos(x),y_2=-sin(x)$

D$.y_1=e^x,y_2=e^x$

E$.y_1=sin(x),y_2=cos(x)$

E$.y_1=sin(x)cos(x),y_2=cos(x)-sin(x)$

G$.y_1=e^{-x},y_2=e^{-x}$