We need to check for all regions: $ x >= 0, y >= 0 $ $ x >= 0, y < 0 $ $ x < 0, y >= 0 $ $x < 0, y < 0 $ However, once we find out the answer for any one of the regions, we do not need to calculate for other regions since the options suggest that there will be a single answer. Let us start with $x >= 0$, $y >= 0$ $ 3x + 3y = 7 $ $2x + 3y = 1 $ Hence, $x = 6 $and $ y = -11/3 $ Since $y > = 0$, this is not satisfying the set of rules. Next, let us test $x >= 0$, $y < 0$ $3x - y = 7$ $2x + 3y = 1$ Hence, $y = -1 $ $x = 2$. This satisfies both the conditions. Hence, this is the correct point. We need the value of $x + 2y$