Solve the system: 1/2x + 1/3y = 5 and x - y = 3. What is the value of y?

Clear the fractions in the first equation by multiplying by $6$: $3x+2y=30$. From the second equation, $x=y+3$. Substitute: $3(y+3)+2y=30$, so $5y+9=30$ and $y=\frac{21}{5}=4.2$, choice B. Then $x=7.2$, and the check is $\frac{1}{2}(7.2)+\frac{1}{3}(4.2)=3.6+1.4=5$. Choice A ($3.6$) is the value of $\frac{1}{2}x$, not of $y$. Choice C ($4.8$) and choice D ($5.4$) come from slips when distributing the $3$ across $(y+3)$, so they fail to satisfy the first equation. Substituting back into both equations is the best way to confirm.