Chapter 3.2, Problem 19PPS

To determine

To Find: the vertices of the triangle formed by the system of inequalities $y\ge 3x-7,y\le 8\text{and}x\text{+}y>1$

Answer to Problem 19PPS

  $\left(-7,8\right),\left(5,8\right)\text{ and }\left(2,-1\right)$

Explanation of Solution

Given

Given inequalities are.

  $y\ge 3x-7,y\le 8\text{and}x\text{+}y>1$ .

Calculation:

Drawing the graph of inequality $y\le 8$ .

Shade the region below the passing parallel to x-axis through $y=8$ .

Drawing the graph of inequality $x\text{+}y>1$ .

On simplifying $x\text{+}y>1$ .

  $\begin{array}{l}x\text{+}y>1\\ y>1-x\end{array}$

Plot the coordinates of equation $y=1-x$ .

  $\begin{array}{cc}x& y\\ 0& 1\\ 1& 0\end{array}$

Shade the region above the line as $y>1-x$ .

Drawing the graph of inequality $y\ge 3x-7$ .

Plot the coordinates of equation $y=3x-7$ .

  $\begin{array}{cc}x& y\\ 0& -7\\ \frac{7}{3}& 0\end{array}$

Shade the region above the line as $y\ge 3x-7$ .

  

From the above graph, vertices of triangle formed are $\left(-7,8\right),\left(5,8\right)\text{ and }\left(2,-1\right)$

So,the answer is $\left(-7,8\right),\left(5,8\right)\text{ and }\left(2,-1\right)$