\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus

Please login to create an exam or a quiz.

Algebra
Linear Systems
New Random

Solve the linear system \(\displaystyle \begin{cases} 5 x - 9 y - 3 z = -153 \\ 5 x + 4 y + 7 z = 54 \\ - 5 x + 8 y - 5 z = 72 \\ \end{cases}\)


The Solution is \(\displaystyle (-9, 9, 9)\).

Download \(\LaTeX\)

\begin{question}Solve the linear system 
$\begin{cases}
	 5 x - 9 y - 3 z = -153 \\ 
	 5 x + 4 y + 7 z = 54 \\ 
	 - 5 x + 8 y - 5 z = 72 \\ 
\end{cases}$
    \soln{9cm}{The Solution is $(-9, 9, 9)$.}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}
HTML for Canvas
<p> <p>Solve the linear system 
 <img class="equation_image" title=" \displaystyle \begin{cases}
	 5 x - 9 y - 3 z = -153 \\ 
	 5 x + 4 y + 7 z = 54 \\ 
	 - 5 x + 8 y - 5 z = 72 \\ 
\end{cases} " src="/equation_images/%20%5Cdisplaystyle%20%5Cbegin%7Bcases%7D%0A%09%205%20x%20-%209%20y%20-%203%20z%20%3D%20-153%20%5C%5C%20%0A%09%205%20x%20%2B%204%20y%20%2B%207%20z%20%3D%2054%20%5C%5C%20%0A%09%20-%205%20x%20%2B%208%20y%20-%205%20z%20%3D%2072%20%5C%5C%20%0A%5Cend%7Bcases%7D%20" alt="LaTeX:  \displaystyle \begin{cases}
	 5 x - 9 y - 3 z = -153 \\ 
	 5 x + 4 y + 7 z = 54 \\ 
	 - 5 x + 8 y - 5 z = 72 \\ 
\end{cases} " data-equation-content=" \displaystyle \begin{cases}
	 5 x - 9 y - 3 z = -153 \\ 
	 5 x + 4 y + 7 z = 54 \\ 
	 - 5 x + 8 y - 5 z = 72 \\ 
\end{cases} " /> </p> </p>
HTML for Canvas
<p> <p>The Solution is  <img class="equation_image" title=" \displaystyle (-9, 9, 9) " src="/equation_images/%20%5Cdisplaystyle%20%28-9%2C%209%2C%209%29%20" alt="LaTeX:  \displaystyle (-9, 9, 9) " data-equation-content=" \displaystyle (-9, 9, 9) " /> .</p> </p>