Answer
The point $(2,3)$ is the solution of the system.
Work Step by Step
Given: $2x+4y \leq 17$ and $6x+5y \leq 29$
Plug $x=2$ and $y=3$ in the inequality $4x-2y \geq 1$
I. $2(2)+4(3) \leq 17$
or, $4+12 \leq 17$
Thus $16 \leq 17$
II. $6(2)+5(3) \leq 29$
or, $12+15 \leq 29$
Thus, $27 \leq 29$
Hence, the point $(2,3)$ is the solution of the system.
