Since you are new to Latex and your knowledge is limited, I recommend you to use the exam package and read the documentation. It is a lot more compatible with what you are doing and will for sure help you in assignment solutions as well as exam question/solutions preparation ;). Now, I have read your previous question as well as this one and came a solution to all of your requirements. Using the exam package will automatically solve some of your desires and will make the logic of your code a lot more simpler.
- You wanted to display 1-4 instead of 14. This can be simply achieved
by doing
1 {}-{} 4 or 1 -- 4 (1 -- 4 will create a longer
dash).
- Aligning numbers, operators, etc. is achieved via the
alignedat environment from the amsmath package.
- Having multiple columns for the answers and/or questions is achieved by
multicols environment from the multicol package.
Now for the final code, I have commented as much as I can and hopefully it all make sense. Oh just one thing, keep in mind that ~ will create a space (LaTeX is very picky with spaces). Hitting the space-bar three times will not output 3 spaces, but only one. Instead, typing ~~~ will register 3 spaces exactly. I have used tildes many times.
page 2
\documentclass[answers,12pt]{exam}
\usepackage{amsmath} % Uses alignedat environment.
\usepackage{multicol} % Allows muliple columns.
\usepackage{enumitem} % Used for alphabetizing lists
% (and using roman numerals in lists).
% To use the aforementioned features
% when using this package in
% \begin{enumerate}[label=(\alph*)]
% (or \Alph* for uppercase or \roman*).
%\usepackage[fleqn]{amsmath} % [fleqn] used in co-ordinance with
% \begin{aligned}[t] to allow equations
% to align left neatly regardless of
% their width.
\usepackage{amssymb}
\usepackage{geometry}
\usepackage{cancel}
\author{Isaac King}
\title{1.1 Systems of Linear Equations}
% Use \Add \Sub \Eq instead of + - =, respectively in mathmode.
% It is Case Sensitive! Those are used to insert space
% between the sign i.e. ~+~. Also, the {}+{} are used to pad
% empty atoms at either side of the operation.
% This is needed to guarantee the desired aligning.
\newcommand{\Add}{\mathbf{{}~+~{}}}
\newcommand{\Sub}{\mathbf{{}~-~{}}}
\newcommand{\Eq}{\mathbf{{}~=~{}}}
% When it mathmode, use \Comment{comment to display}
% for displaying your comments.
\newcommand{\Comment}[1]{\quad \text{#1}}
% Create the horizontal line when adding two addition
\newcommand{\Line}[2]{\\[-2ex]\cline{#1-#2}\\[-4.25ex]}
% Uncomment the next line to add a frame around the solution.
\unframedsolutions
\begin{document}
\maketitle
Solve each system in Exercises 1 {}-{} 4 by 1 -- 4 using elementary row
operations on the equations or on the augmented matrix.
Follow the systematic elimination procedure described in this section.
% Enter a question environment and create a question via
% the \question command. Once the question is typed,
% use the \begin{solution}...\end{solution} for the solution.
\begin{questions}
% Question 1
\question This is the first question, solve
$
\begin{alignedat}[t]{3}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5
\end{alignedat}
$
% Question 1 Solution
\begin{solution}
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{Replacement Eq. 2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\end{solution}
% Question 2
\question This is a question and the solution is divided into 2 columns!
% Question 2 Solution
\begin{solution}
\begin{multicols}{2}
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{Eq. 2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
% Now, a new column will start.
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{Eq. 2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\end{multicols}
\end{solution}
% Question 3
\begin{multicols}{2}
% Left item
\question Question on the left side!! Solution on the right!!
% Question 3 Solution
\begin{solution}
\begin{enumerate}[label=(\alph*)]
\item % Top right item
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{E2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\item % Bottom right item
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{E2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\end{enumerate}
\end{solution}
\end{multicols}
% Question 4
\question This is a question and the (labelled!!)
solution is divided into 2 columns!
% Question 4 Solution
\begin{solution}
\begin{multicols}{2}
\begin{enumerate}[label=(\alph*)]
\item % Left item
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{E2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\item % Right item
$
\begin{alignedat}[t]{6}
x_{1} & \Add & 5x_{2} & \Eq & 7\\
-2x_{1} & \Sub & 7x_{2} & \Eq & -5\\\\
2(x_{1} & \Add & 5x_{2} & \Eq & 7) & \Comment{E2}\\
\Add -2x_{1} & \Sub & 7x_{2} & \Eq & -5~ \Line{1}{5}
~ & ~ & 3x_{2} & \Eq & 2~\\
\end{alignedat}\\[10pt]
$
\end{enumerate}
\end{multicols}
\end{solution}
\end{questions}
\end{document}
