Chapter 2.1, Problem 12E

To determine

To find: whether the system is consistent and independent, consistent and dependent, or inconsistent.

Answer to Problem 12E

Inconsistent

Explanation of Solution

Given information:

  $\begin{array}{l}y=0.5x\mathrm{...}\left(1\right)\\ 2y=x+4\mathrm{...}\left(2\right)\end{array}$

Calculation:

The slope intercept equation is as follows:

  $y=mx+b$

Convert equation (1) in slope intercept form and find slope as shown below.

  $y=0.5x+0$

The value of slope for equation (1) is $0.5$ .

Convert equation (2) in slope intercept form and find slope as shown below.

  $\begin{array}{l}2y=x+4\\ y=\frac{1}{2}x+\frac{4}{2}\\ y=0.5x+2\end{array}$

The value of slope for equation (2) is $0.5$ .

Since, the two lines have same value of slopes and are parallel. Thus, the system is inconsistent.