To determine whether $(-1,7)$ is a solution of the system, we substitute $x = -1$ and $y = 7$ into each inequality and check if the inequality is satisfied. For the first inequality, we have \[2x + 5y = 2(-1) + 5(7) = -2 + 35 = 33.\] Since $33 > -6$, the inequality $2x + 5y > -6$ is satisfied by $(-1,7)$. For the second inequality, we have \[-4x + 3y = -4(-1) + 3(7) = 4 +21 = 25.\] Since $25 \leq 2$, the inequality $-4x+3y \leq 2$ is not satisfied by $(-1,7)$. Therefore, $(-1,7)$ is not a solution of the system.
