Question

23: Solve each system of inequalities by graphing.

$\begin{array}{c}y<x+1\\ x>5\end{array}$

Short answer

The solution is$y<x+1$.

Step-by-step solution

Step-1 – 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 – 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 $y<x+1$and$x>5$.

The linear inequation of the respective inequalities are $y=x+1$ and$x=5$.

Point which satisfies the equation $y=x+1$ are $(0,1)$and$(-1,0)$.

Step-4 – Shading the region

We choose $(0,0)$then the point $(0,0)$ satisfies the inequality $y<x+1$but the point does not satisfy the inequality$x>5$.

Step-5 – Plotting the graph

So, the graph of the inequality is

The common region is$y<x+1$.