Step 1 :Let's denote \(6^x=a\) and \(6^y=b\).
Step 2 :Then, the equations become \(a+b=42\) and \(x+y=3\).
Step 3 :From the second equation, we can express \(y\) as \(y=3-x\).
Step 4 :Substitute \(y\) into the first equation, we get \(a+6^{3-x}=42\).
Step 5 :Rearrange the equation, we get \(a=42-6^{3-x}\).
Step 6 :Substitute \(a\) into the second equation, we get \(x+\frac{\log(42-6^{3-x})}{\log(6)}=3\).
Step 7 :Solving this equation, we get \(x=\boxed{2}\) and \(y=\boxed{1}\).
Step 8 :Substitute \(x=2\) and \(y=1\) into the original equations, we find this works.