Q4. - Algebra 2

Question

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

4.$\begin{array}{l}y\ge x+2\\ y\le -2x-1\end{array}$

Step-by-Step Solution

Answer

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

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

We have,

$y=x+2$

If$x=1$, then$y=3.$.

If$x=2$, then$y=4.$.

If$x=3$, then $y=5.$

$\therefore$The points are $\left(1,3\right),\left(2,4\right)$ and $\left(3,5\right).$

For, $y=-2x-1$

If$x=1$, then$y=-2\left(1\right)-1$

                           $y=-3.$

If$x=2$, then$y=-2\left(2\right)-1$.

                          $\begin{array}{l}y=-4-1\\ =-5.\end{array}$

If$x=0$, then $y=-2\left(3\right)-1$

                            $y=-7.$

$\therefore$The points are $\left(1,-3\right),\left(2,-5\right)$ and $\left(3,-7\right).$

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 $y\ge x+2$is away from the origin and the solution of $y\le -2x-1$ is also away from the region. Therefore, the shaded region is the common region that is the solution of inequation.