SOLUTION:

\[\begin{array}{*{35}{l}}

x\text{ }+\text{ }2y\text{ }\le \text{ }3  \\

{}  \\

\end{array}\]

\[Line:\text{ }x\text{ }+\text{ }2y\text{ }=\text{ }3\]

Also, (0, 0) satisfies the\[x\text{ }+\text{ }2y\text{ }\le \text{ }3\] , hence region is towards the origin

\[Line:\text{ }3x\text{ }+\text{ }4y\text{ }=\text{ }12\]

Also, (0, 0) satisfies the\[3x\text{ }+\text{ }4y\text{ }\le \text{ }3\] , hence region is towards the origin

x ≥ 0 ⇒ region is to the right of the y-axis

And, y ≥ 1 ⇒ region is up above the line x = 1,

Hence, we can conclude from the graph that the above system has no common region as solution

.