Can you explain number 7 on P. 72 of PWN the SAT 4th edition? Thank you.

Yep! Use elimination again here. Recognize that if you multiply the first equation by 5, you’ll have the easy opportunity to eliminate the x-terms.

    \begin{align*}5x\sqrt{2}+15y&=65\\-\left(5x\sqrt{2}+20y\right)&=-70\\\rule{2cm}{0.4pt}&\rule{1cm}{0.4pt}\\-5y&=-5\end{align*}

From there, you know that y = 1, so you know the answer must be A because no other choice has 1 for its y-coordinate. Might as well keep solving for x to be sure, though…

    \begin{align*}5x\sqrt{2}+15(1)&=65\\5x\sqrt{2}&=50\\x&=\dfrac{50}{5\sqrt{2}}\\x&=\dfrac{50}{5\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}\\x&=\dfrac{50\sqrt{2}}{10}\\x&=5\sqrt{2}\end{align*}