Question 316405
Supply and demand are both functions of price. At the equilibrium price, supply equals demand. Thus, we are looking for a value of p such that S(p)=D(p). That is, 

{{{(1/6) p = 9 - (1/3) p }}} 

and we must solve for p. 

We can add {{{(1/3)p}}} from both sides to get: 

{{{ (1/6)p + (1/3)p = 9 }}} 

Combining the like terms on the left side gives 

{{{ (1/2) p = 9}}} 

Thus, multiplying by 2 on both sides gives {{{p = 18}}}. 


Now we check: at p = 18, S(p)={{{(1/6) 18 = 3}}} and D(p)={{{9-(1/3)18=9-6=3}}}, so the supply and demand are both equal to 3.