The critical points of the system $\frac { d x } { d t } = 2 x + y - 3 , \frac { d y } { d t } = 2 x - 3 y - 7$ are
A) $y = - 1$
B) $x = 2$
C) $( 2 , - 1 )$
D) $( - 1,2 )$
E) $( - 3 , - 7 )$

Question

Quizplus · Accepted Answer

Critical points occur where the derivatives $dx/dt$ and $dy/dt$ are both zero. Solving the system $2x + y - 3 = 0$ and $2x - 3y - 7 = 0$ simultaneously gives the solution $(x, y) = (2, -1)$.

The Critical Points of the System dxdt=2x+y−3,dydt=2x−3y−7\frac { d x } { d t } = 2 x + y - 3 , \frac { d y } { d t } = 2 x - 3 y - 7dtdx​=2x+y−3,dtdy​=2x−3y−7

The Critical Points of the System $\frac { d x } { d t } = 2 x + y - 3 , \frac { d y } { d t } = 2 x - 3 y - 7$