Chapter 2.1, Problem 13E

To determine

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

Answer to Problem 13E

Consistent and dependent

Explanation of Solution

Given information:

  $\begin{array}{l}-35x+40y=55\mathrm{...}\left(1\right)\\ 7x=8y-11\mathrm{...}\left(2\right)\end{array}$

Calculation:

The slope intercept equation is as follows:

  $y=mx+b$

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

  $\begin{array}{c}-35x+40y=55\\ 40y=35x+55\\ y=\frac{35}{40}x+\frac{55}{40}\\ y=\frac{7}{8}x+\frac{11}{8}\end{array}$

The value of slope for equation (1) is $\frac{7}{8}$ .

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

  $\begin{array}{c}7x=8y-11\\ 8y=7x+11\\ y=\frac{7}{8}x+\frac{11}{8}\end{array}$

The value of slope for equation (2) is $\frac{7}{8}$ .

Since, the two lines have same value of slopes and both the equations are same. That is, they have infinite number of solutions. Thus, the system is consistent and dependent.