Question

4x + y< 2

Answer 1

The two inequalities can be rewritten as

$\begin{cases}y-2\end{cases}$

The solution is composed by every point below the graph of the line $y=-4x+2$, and above the horizontal line $y=-2$

To draw the line $y=-4x+2$ we can build a little table (only 2 points are required):

$\begin{array}{c|c}x&y\\0&2\\1&-2\end{array}$

So, if you draw the points (0,2) and (1, -2) and connect them, you'll have your line.

To draw the line $y=-2$, simply pick any point with y coordinate -2, for example (0, -2), and draw a horizontal line.

Choose the above/below areas as specified above to solve the system.