Question

22: Solve each system of inequalities by graphing.

$\begin{array}{c}\left|y\right|>3\\ x\le 1\end{array}$

Short answer

The solution is $\left|y\right|>3$ and$x\le 1$.

Step-by-step solution

Step-1 – Concept of solution of linear inequalities

The solution of linear inequalities can be obtained by changing the inequalities into equations and solving the linear equations to obtain a graph. Then the common shaded region is a solution of the inequalities.

Step-2 – 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 – Evaluation of solution

The two inequalities are $\left|y\right|>3$ and$x\le 1$.

The linear inequations of the respective inequalities are $\left|y\right|=3$ and $x=1$

$y=3$or$y=-3$,$x=1$.

Step-4 – Shading the region

We choose $(0,0)$then the point $(0,0)$satisfies the inequality $x\le 1$ but it does not satisfy the inequalities$\left|y\right|>3$.

Step-5 – Plotting the graph

So, the graph of the inequality is

The common region is $\left|y\right|>3$ and$x\le 1$