What is the value of $2x+3y$ if $x+y=7$ and $x^2-y^2=21$? If $x+y=7$ and $x^2-y^2=21$, then what is $2x+3y$?
I solved it like this:
\begin{align}
y& =7-x \\
x^2-(7-x)^2-21&=0 \\
x^2-49+14x-x^2-21&=0 \\
14x&=70 \\
x&=5 
\end{align}
Then I solved for $y$ and I got $2$. I plugged in the values of $x$ and $y$ to $2x+3y$, and I got $16$.
Is this correct?

Quicker way is to note that
$$
21=(x-y)(x+y)=7(x-y)
$$
so
$$
x-y=3
$$
Combined with $x+y=7$, we get that $2x=10$ i.e. $x=5$ and $y=2$.
So your answer is correct.
