#### Chapter 4 System of Linear Equations

Section 4.3 LS in three Variables

# 4.3.5 Exercises

##### Exercise 4.3.10
Find the solution set of the following system of linear equations

$\begin{array}{ccc}\multicolumn{1}{c}{2x-y+5z}& =\hfill & 1 ,\hfill \\ \multicolumn{1}{c}{11x+8z}& =\hfill & 2 ,\hfill \\ \multicolumn{1}{c}{-4x+y-3z}& =\hfill & -1\hfill \end{array}$

using
1. the substitution method,

##### Exercise 4.3.11
Consider the following circuit: It consists of a source providing a voltage of $U=5.5 \mathrm{V}$ and three resistors ${R}_{1}=1 \mathrm{}\Omega$, ${R}_{2}=2 \mathrm{}\Omega$, and ${R}_{3}=3 \mathrm{}\Omega$. Find the currents ${I}_{1}$, ${I}_{2}$, and ${I}_{3}$ in the loops.
Hints: The relations between voltages, resistances, and currents in such circuits are described by the so-called Kirchhoff's rules which in this example result in the following three equations:

Additionally, the relation between the physical units Volt ($\mathrm{V}$) (voltage), Ampère ($\mathrm{A}$) (current) und Ohm ($\Omega$) (resistance) is used: $1 \mathrm{}\Omega =\left(1 \mathrm{V}\right)/\left(1 \mathrm{A}\right)$.

##### Exercise 4.3.12
Find the solution set of the following system of equations using the addition method:

$\begin{array}{ccc}\multicolumn{1}{c}{x+2z}& =\hfill & 5 ,\hfill \\ \multicolumn{1}{c}{3x+y-2z}& =\hfill & -1 ,\hfill \\ \multicolumn{1}{c}{-x-2y+4z}& =\hfill & 7 .\hfill \end{array}$