Question

Solve each system of equations by graphing.

24.$\begin{array}{l}y\le x+4\\ 2y\ge x-3\end{array}$

Short answer

The solution of the inequality is $y-4\le x\le 2y+3.$

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 inequality

The shaded region obtained by choosing a point if the point satisfies the inequality the region is along the point if it not satisfies the inequality than the shaded region is opposite to the point.

Step-3 –Evaluation of solution

The two inequalities are$y\le x+4$and $2y\le x-3.$

The linear equation of the respective inequalities are $y=x+4$and $2y=x-3.$

Points which satisfy the equation $y=x+4$are $\left(0,4\right)$and$\left(-4,0\right)$.

Points which satisfy the equation $2y=x-3$are $\left(3,0\right)$and $\left(1,-1\right)$.

Step-4 –Shading the region

We choose the point$\left(0,0\right)$.

The point$\left(0,0\right)$satisfy both the inequalities $y-4\le x\le 2y+3.$

Step-7–Plotting the graph

So, the graph of the inequality is

The common region is $y-4\le x\le 2y+3.$