Answer
False
Work Step by Step
The system of differential equations $x′=-2x$, Because it is in form
$\frac{dx_1}{dt}=a_{11}(t)x_1(t)+a_{12}(t)x_2(t)+...+a_{1n}(t)x_n(t)+b_1(t)$ where $a_{ij}(t)$ and $b_i(t)$ are specified functions on an interval $I$.
But $y′ =e^yx+e^ty$ is not a first-order linear system of differential equations. It should be $y′ =e^tx+e^ty$
