Solving Linear Systems

We begin by examining the lines as boundary lines to the shaded region. We see that the edge of the area consists of a vertical line along with the $y$-axis, a horizontal line along the $x$-axis, and a dashed line. Let's extend these lines.

The horizontal line can be described with the equation $y=0$ and the vertical line is given by $x=0.$ To find the equation of the dashed line we can mark the slope and the $y$-intercept. Then, the equation can be written in slope-intercept form.

Now we have the equations of the three boundary lines representing the region. The next step is to write inequalities for each equation to form a system of inequalities. We see that the shaded area is below, but not on, the line $y=\text{-}x+4,$ which means that the first inequality is $$y<\text{-}x+4.$$ The area is also located to the right of $x=0.$ This means it's all $x$-values greater than or equal $0.$ $$x\ge 0.$$ Finally, the area also above, and on, the line $y=0.$ Together these three inequalities describes the shaded region. $$\{\begin{array}{l}y<\text{-}x+4\\ x\ge 0\\ y\ge 0\end{array}$$