Q1. - Algebra 2

Question

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

$\begin{array}{l}y\ge 4\\ y\le -x\end{array}$

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 inequation.

For,$y=4$

Since, the line is parallel to $x$-axis which intersect $y$-axis at $4$.

For, $y=-x$

If $x=1$, then$y=-1$.

If $x=2$, then$y=-2$.

If $x=3$, then $y=-3.$

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

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 $y\ge 4$ is away from the origin and the solution of $y\le -x$ is also away from the origin. Therefore, the shaded region is the common region that is the solution of inequation.