Question 788611
{{{x}}}= amount of acid added (in liters)
{{{y}}}= amount of 10% solution you start with (in liters)
 
One equation is the balancing of total amounts (in liters) 
{{{x+y=27}}}
 
The other equation is the balancing of the amount of pure acid:
{{{0.1y+x=0.2*27}}}<-->{{{0.1y+x=5.4}}}<-->{{{10x+y=54}}}
Since you start with {{{y}}} liters of 10% acid, you are starting with 10% of {{{y}}} liters of pure acid in that solution, or
{{{0.1y}}}
You add {{{x}}} liters of pure acid, and end up with 27 liters of a 20% acid solution that must contain 20% of 27 liters of pure acid, or
{{{0.2*27}}}
 
Your system could be
{{{system(x+y=27,x+0.1y=5.4)}}} or {{{system(x+y=27,10x+y=54)}}}
 
NOTE:
As a chemist, I find this kind of problem offensively wrong in more ways than I care to count, but since I can't beat them, I may as well join them and pretend that it makes sense.