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\documentclass[12pt,letterpaper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage{array}
\usepackage{booktabs}
%Is there an easier way to make horizontal lines in tables than using the booktabs package?
\title{What is a ``Solution" to a System of Equations?}
\date{}
\author{\LaTeX\ Learner}
\begin{document}
\maketitle
%All 3 of the vspaces below are 5pt. Why isn't the vertical spacing consistent?
\noindent \textbf{The System}
\vspace{5pt}
\noindent Equation 1: $5x+3y=9$\\
\vspace{5pt}
\noindent Equation 2: $-4y+10=x+15$
\vspace{5pt}
%Why don't the borders of the tables touch? And why does it give me errors when I try to put "\midrule" anywhere else, e.g. line 42 or 44?
\begin{tabular}{|p{5cm}|p{2.5cm}|p{2.5cm}|p{2.5cm}|}
\midrule
Possible Solution&\raggedright Solution to Equation 1?&\raggedright Solution to Equation 2?& \raggedright Solution to The System? \\
%Why the heck are all these equations in the column farthest to the right? How do I put them in the left-most column?
$x=2, y=5$\\
$$x=1, y=2$$\\
$$x=3, y=-2$$\\
$$(-2,3)$$\\
$$(-5,0)$$\\
\end{tabular}
\begin{enumerate}
\item What is the solution to the system?
\item How can you tell if you have a solution to a system?
\item The system of equations above has \_\_\_\_ equations. A solution has to satisfy \_\_\_\_ of them.
\item If a system of equations has 25 equations, then a solution must satisfy \_\_\_\_ of them.
\item If a system of equations has $n$ equations, its solution must satisfy \_\_\_\_ of them.
\end{enumerate}
%How do I make the blank spaces for writing a continuous line instead of four small separated underscores?
\pagebreak
\noindent \textbf{Another System of Equations}
%Again, what's with the inconsistent spacing here?
\vspace{5pt}
\noindent Equation 1: $x-2y=-11$\\
\vspace{5pt}
\noindent Equation 2: $3x=2y-13$\\
\vspace{5pt}
\noindent Decide if the following are solutions to the system above or not.
\begin{itemize}
\item $x=-3, y=4$
\item $(-1,5)$
\item %Easiest way to draw an x-y plane graph from (-5,-5) to (5,5) with a dot on (1,4)?
\end{itemize}
\end{document}