I'm probably making a silly mistake or Wolfram Alpha is lying to me.

Question: Find the value of c and d.

$\displaystyle 3d=13-2c$

$\displaystyle \frac{3c+d}{2}=8$

Rearranged, simplified and multiply each equation by 2:

$\displaystyle 6d+4c=26$

$\displaystyle d+3c=16$

Now find the common multiple which in my case I will use 12:

$\displaystyle 18d+12c=78$

$\displaystyle -4d-12c=-64$

Then add them and find what d is worth:

$\displaystyle 14d=14$

$\displaystyle d=1$

Now when I plug this back into the equation, I will use the first one:

$\displaystyle 3(1)+2c=13$

$\displaystyle 3+2(c)=13$

$\displaystyle c=5$

$\displaystyle d=1, c=5$

What am I doing wrong? Sorry if this is the long winded way to do it.