Question

Solve each system of inequalities. Sketch each graph on a sheet of paper.

$\begin{array}{l}y\ge 1-x\\ y\le x+5\end{array}$

Short answer

The shaded region is the solution of the given inequations, which is unbounded.

Step-by-step solution

Step-1 –Apply the concept of linear equation to solve the linear inequation.

We have,

$y=1-x$

If$x=1$, then$y=0$.

If$x=2$, then$y=-1$.

If$x=0$, then $y=1.$

$\therefore$The points are $\left(1,0\right),\left(2,-1\right)$and $\left(0,1\right).$

For, $y=x+5$

If$x=1$, then$y=6$.

If$x=-2$, then$y=3$.

If$x=0$, then $y=5.$

$\therefore$The points are $\left(1,6\right),\left(-2,3\right)$and $\left(0,5\right).$

Step-2–Plot the point on the graph paper and form a region of each inequation

Step-3–Identifying the common region

Since, the solution of $y\ge 1-x$is away from the origin and the solution of $y\le x+5$is towards the origin. Therefore, the shaded region is the common region that is the solution of inequation.