Question

Can someone show me how to do this:

Answer 1

The first and second problems involve the same process. If you're not sure how to graph inequalities, start by graphing the lines.
\[\begin{cases}x+2y=6\\
x=2\\y=1\end{cases}\]
Here's what we get:

Answer 2

Consider one line at a time. For the oblique one, \(x+2y\le6\), let's pick an arbitrary point in the plane and test that value. If the inequality holds, then the region containing this point will be the shaded region.

For example, suppose we take \((0,0)\), which means we plug in \(x=0\) and \(y=0\). If \(x+2y\le6\), then the entire region below the line will be shaded because \((0,0)\) is located below the line.
\[0+2(0)=0\le6\implies\text{TRUE}\]