Chapter 2.3, Problem 56E

To determine

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

Answer to Problem 56E

Consistent and dependent

Explanation of Solution

Given information:

The given system of equations is as follows:

  $4x-2y=7$... (1)

  $-12x+6y=-21$... (2)

Calculation:

Multiply equation (1) by 3 and solve as follows:

  $\begin{array}{l}\left(4x-2y=7\right)\left(3\right)\\ 12x-6y=21\mathrm{...}\left(3\right)\end{array}$

Use elimination method to solve equation (3) and (2) as follows:

  $\begin{array}{l}12x-6y=21\\ -12x+6y=-21\\ \overline{0+0=0}\\ 0=0\end{array}$

System has solution, but there is no unique solution. This means that the given system is consistent but dependent.