Chapter 13.6, Problem 34WE

a.

To determine

To graph: on the same axes.

Explanation of Solution

Given information: The equations are $y=-2,x=-3\&2x+3y=6$ .

Graph:

The graph will be:

  

Interpretation:

From the above graph it is observed that the blue line represents $2x+3y=6$ , the green line represent $x=-3$ and the black line represent $y=-2$ .

b.

To determine

To find: the coordinate where the lines intersect.

Answer to Problem 34WE

The coordinates are $\left(-3,4\right)\&\left(6,-2\right)$ .

Explanation of Solution

Given information: The equations are $y=-2,x=-3\&2x+3y=6$ .

Calculation:

The intersection of $x=-3\&2x+3y=6$ is $\left(-3,4\right)$ .

The intersection of $y=-2\&2x+3y=6$ is $\left(6,-2\right)$ .

c.

To determine

To find: the area of the triangle.

Answer to Problem 34WE

The area of triangle is $27$ .

Explanation of Solution

Given information: The equations are $y=-2,x=-3\&2x+3y=6$ .

Calculation:

  $x=-3\&y=-2$ are perpendicular.

So, it’s a right angle triangle.

Base $=9$

Height $=6$

Area $=\frac{1}{2}\times \text{base}\times \text{height}$

  $\begin{array}{l}\Rightarrow =\frac{1}{2}\times \text{6}\times \text{9}\\ \Rightarrow 27\end{array}$