Chapter 8.8, Problem 30E

To determine

To choose: the correct option that represents the equivalent equations.

Answer to Problem 30E

A. I and II only

Explanation of Solution

Given information:

The equations are as follows:

  $\begin{array}{l}\text{I}\text{. }2x+4y=8\\ \text{II}\text{. }3x+6y=12\\ \text{III}\text{. }4x+8y=8\\ \text{IV}\text{. }6x+12y=16\end{array}$

The options are as follows:

1. I and II only
2. I and IV only
3. II and IV only
4. III and IV only
5. I, II and III

Calculation:

Simplify each equation as shown below.

  $\text{I}\text{. }2x+4y=8$

  $x+2y=4\left[\text{Divide each side by 2}\right]$

  $\text{II}\text{. }3x+6y=12$

  $x+2y=4\left[\text{Divide each side by 2}\right]$

  $\text{III}\text{. }4x+8y=8$

  $x+2y=2\left[\text{Divide each side by 4}\right]$

  $\text{IV}\text{. }6x+12y=16$

  $x+2y=\frac{8}{3}\left[\text{Divide each side by 6}\right]$

Since equation I and II are equivalent, so option A. is correct.