title: How can I find the different points of a system of equations?
body: <p>I've got to solve this system of equations:</p>
  <blockquote>
  <p>aQ + bP = c<br />
  dQ + eP = f</p>
  </blockquote>
  <p>I have to find 100 values Q and P that solve the systems with 100 randomly drawn coefficients from the following distributions:</p>
  <blockquote>
  <p>a ~ N( 100; 10)</p>
  <p>b ~ N(-1;0.1)</p>
  <p>c ~ N(10;1)</p>
  <p>d ~ N(10;0.1)</p>
  <p>e ~ N(100;10)</p>
  <p>f ~ N(10;0.1)</p>
  </blockquote>
  <p>Which I did by doing the following:</p>
  <pre><code>a&lt;-rnorm(100,mean=100,sd=10)
  b&lt;-rnorm(100,mean=-1,sd=.1)
  c&lt;-rnorm(100,mean=10,sd=1)
  d&lt;-rnorm(100,mean=10,0.1)
  e&lt;-rnorm(100,mean=100,sd=10)
  f&lt;-rnorm(100,mean=10,0.1)
  </code></pre>
  <p>Then I made matrix:</p>
  <pre><code>O &lt;- matrix(data=c(a,b,c),1,1)
  P&lt;- matrix(c(d,e,f),1,1)
  </code></pre>
  <p>Finally solved it using:</p>
  <pre><code>solve(O,P)
  </code></pre>
  <p>My problem is that I'm trying to get 100 solutions but this code returns just one solution. After obtaining the 100 values for Q and P I need to make a plot with all of the values.</p>