title: Maxima: how to replace variables in equations
body: <p>I'm trying to write down some notes of my work. The way Maxima would simplify my work is that once I write bunch of equations and I want to change the definition of a variable, I do it and re-evaluate the entire file.</p>
  
  <p>Here is an example of what I'm trying to accomplish:</p>
  
  <hr>
  
  <p>Question 1:
  I have a system of equations and all I want from Maxima is just variables replacement.</p>
  
  <pre><code>eq1: x=a+b+c
  eq2: y=d+e+f
  eq3: x+y=0
  </code></pre>
  
  <p>How do I get Maxima to output</p>
  
  <pre><code>eq3: a+b+c+d+e+f = 0
  </code></pre>
  
  <p>So in the future if I want x to be a+b-c, I just change it and re-evaluate</p>
  
  <hr>
  
  <p>Question 2:
  Similar to before but a bit more complex</p>
  
  <pre><code>eq1: x=a+b+c
  eq2: y=d+e+f
  eq3: x=y
  eq4: a+s+e=0
  </code></pre>
  
  <p>How do I get Maxima to output</p>
  
  <pre><code>eq3 a+b+c=d+e+f
  </code></pre>
  
  <p>How do I get Maxima to solve eq1 for a and solve eq2 for e and output</p>
  
  <pre><code>eq4: x-b-c+s+y-d-f = 0
  </code></pre>
  
  <p>Thank you in advance for your help,
  Guido</p>