Chapter 13, Problem 37RP

To determine

To find: The intersection point for the given equation.

Answer to Problem 37RP

The point of intersection for the given equations is $\left(2,14\right),\left(-26,42\right)$ .

Explanation of Solution

Given:

The given equation is,

  $\begin{array}{l}x+y=16\\ y=\left|2x+10\right|\end{array}$

Calculation:

Consider the given equations are,

  $\begin{array}{l}x+y=16\\ y=\left|2x+10\right|\end{array}$

The equation is re written as,

  $\begin{array}{l}y=-x+16\\ y=2x+10\\ y=-2x-10\end{array}$

Then, solve for $x$ as,

  $\begin{array}{l}y=-x+16\\ 2x+10=-x+16\\ 3x=6\\ x=2\end{array}$ And $\begin{array}{l}y=-x+16\\ -2x-10=-x+16\\ -x=26\\ x=-26\end{array}$

Solve for $y$ as,

  $\begin{array}{c}y=2x+10\\ =2\left(2\right)+10\\ =14\end{array}$ And $\begin{array}{c}y=2x+10\\ =2\left(-26\right)+10\\ =42\end{array}$

Thus, the point of intersection for the given equations is $\left(2,14\right),\left(-26,42\right)$ .