Q21. - Algebra 2

Question

21: Solve each system of inequalities by graphing.

$\begin{array}{c}y\le 4\\ y>-3\end{array}$

Step-by-Step Solution

Answer

The solution is$-3<y\le 4$.

Step-1 &ndash; Concept of solution of linear inequalities

The solution of the inequalities can be obtained by changing the inequalities into equations and solving the linear equations.

Step-2 &ndash; Concept of shading the region of the inequalities

The shaded region obtained by choosing a point, if the point satisfies the inequality the region is along the point, if not satisfies the inequalities, then the shaded region is opposite to the point.

Step-3 &ndash; Evaluation of solution

The two inequalities are $y\le 4$ and $y>-3$.

The linear equations of the respective inequalities are $y=4$ and $y=-3$.

Step-4 &ndash; Shading the region

We choose $(0,0)$then the point $(0,0)$ satisfies the inequality $y\le 4$ as well as$y>-3$.

Step-5 &ndash; Plotting the graph

So, the shaded region can be plotted as

The inequality represents the shaded region is$-3<y\le 4$