Q2. - Algebra 2

Question

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

 $\begin{array}{l}y\ge -2x\\ y\le -3\end{array}$

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, $y=-2x$

If $x=0$, then$y=0$.

If $x=1$, then$y=-2$.

If $x=2$, then $y=-4.$

$\therefore$The points are $\left(0,0\right),\left(1,-2\right)$ and $\left(2,-4\right).$

For, $y=-3$

Since, the line is parallel to $x$-axis which intersect the $y$-axis at $-3.$

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 $y=-2x$ is away from the origin and the solution of $y=-3$ is also away from the origin. Therefore, the shaded region is the common region that is the solution of inequation.