Chapter 6.1, Problem 46PPS

a.

To determine

To find: Solve the given equation.

Answer to Problem 46PPS

  $x=6$

Explanation of Solution

Given information:

  $\frac{1}{2}x+3=-x+12$

Given

  $\frac{1}{2}x+3=-x+12$

On solving

We get

  $\begin{array}{l}\frac{1}{2}x+3=-x+12\\ \Rightarrow \frac{1}{2}x+x=12-3\\ \Rightarrow \frac{x+2x}{2}=9\\ \Rightarrow \frac{3x}{2}=9\\ \Rightarrow x=9\times \frac{2}{3}\\ \Rightarrow x=3\times 2\\ \Rightarrow x=6\end{array}$

Therefore,

  $x=6$

b.

To determine

To find: Using graph solve the given equation.

Answer to Problem 46PPS

  $\left(6,6\right)$

Explanation of Solution

Given information:

  $\begin{array}{l}y=\frac{1}{2}x+3\\ y=-x+12\end{array}$

Given

  $\begin{array}{l}y=\frac{1}{2}x+3\\ y=-x+12\end{array}$

Graph of given equations are

  

Here red line represents the line of $y=\frac{1}{2}x+3$

Blue line represents the line of $y=-x+12$

Point of intersection is the solution of both equations i.e $\left(6,6\right)$

c.

To determine

To find: How is equation in part a related to the system in part b.

Explanation of Solution

Given information:

  $\frac{1}{2}x+3=-x+12$

Both sides of the equation in part a are set equal to $y$ in the system of linear equations in part b.

Both equations are almost similar.

d.

To determine

To find: Explain how to use the graph in part b to solve the equation in part a.

Explanation of Solution

Given information:

  $\frac{1}{2}x+3=-x+12$

You can use the graph to find the x-coordinate of the intersection of the two.

Then, you can substitute that value into the equation in part a and see if it checks.