我想让这个演示在数学上更令人愉悦 - 也就是说,我想让这个在职的过程,这样第一个和第二个之间就没有太大的区别
7\left(\frac 1 2 y\right) + 8y &= 9 \\
和第二行
-7y + 16y &= 18 \\
我也考虑过使用,\iff
但不确定如何正确对齐。我也非常感激有关数学表示的任何反馈。
\textbf{Example 1.} \\
In the following system, first equation has $u_1 = 7$ and \emph{common difference} $d = 1$. Second equation has the \emph{common difference} $d = - 3$ and starts with $u_1 = 6$
\begin{align*}
7x + 8y &= 9 \\
6x + 3y &= 0
\end{align*}
Expressing $ x = - \frac 1 2 &y$ from the second equation and substituting into the first one, we get
\begin{align*}
7\left(\frac 1 2 y\right) + 8y &= 9 \\
-7y + 16y &= 18 \\
9y &= 18 \\
y &= 2
\end{align*}
From here, we substitute back into second equation and obtain $x = -1$.
答案1
你可以使用两个对齐点而不是一个。我还添加了第二种方法来解决这个问题用途价值你1在两个方程中。提及这些值却从不使用它们是没有意义的。
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\theoremstyle{definition}
\newtheorem{example}{Example}
\begin{document}
\begin{example}
In the following system, the first equation has $u_1 = 7$ and
\emph{common difference} $d = 1$. The second equation has the \emph{common difference}
$d = - 3$ and starts with $u_1 = 6$
\begin{align*}
7x + 8y &= 9 \\
6x + 3y &= 0
\end{align*}
Expressing $ x = - \frac{1}{2}y$ from the second equation and substituting
into the first one, we get
\begin{alignat*}{2}
7\left(\frac{1}{2}y\right) &+{}& 8y &= 9 \\
-7y &+{}& 16y &= 18 \\
& & 9y &= 18 \\
& & y &= 2
\end{alignat*}
From here, we substitute back into the second equation and obtain $x = -1$.
\end{example}
\begin{example}
In the following system, the first equation has $u_1 = 7$ and
\emph{common difference} $d = 1$. The second equation has the \emph{common difference}
$d = - 3$ and starts with $u_1 = 6$
\begin{align*}
7x + 8y &= 9 \\
6x + 3y &= 0
\end{align*}
Multiplying the first equation by $6$, the second by $7$ and subtracting, we get
\begin{align*}
42x + 48y &= 54 \\
42x + 21y &= 0 \\[1ex]
27y&=54
\end{align*}
hence $y=2$. From here, we substitute back into the second equation and obtain $x=-1$.
\end{example}
\end{document}
我还添加了一个适当的环境用于示例。避免\frac 1 2 y
。如果您开始使用分子或分母较大的分数,则很难阅读并可能导致输出不佳:\frac 11 2
不会产生预期的结果,是吗?
答案2
这个建议适合你吗?
\documentclass{article}
\usepackage{nccmath, mathtools}
\begin{document}
\textbf{Example 1.} \\
In the following system, first equation has $u_1 = 7$ and \emph{common difference} $d = 1$. Second equation has the \emph{common difference} $d = - 3$ and starts with $u_1 = 6$
\begin{align*}
7x + 8y &= 9 \\
6x + 3y &= 0
\end{align*}
Expressing $ x = - \frac 1 2y$ from the second equation and substituting into the first one, we get
\begin{alignat*}{2}
7\left(\mfrac 1 2 y\right) & + {} & 8y &= 9 \\[-1.5ex]
& \Updownarrow &\\[-1ex]
-7y & +{} & 16y & = 18 \\
&& 9y &= 18 \\
& & y &= 2
\end{alignat*}
From here, we substitute back into second equation and obtain $x = -1$.
\end{document}