Can you explain number 9 on P. 72 of PWN the SAT 4th edition?

Sure. Recognize that \sqrt{45} simplifies to 3\sqrt{5}, so you can rewrite the first equation thusly: 2x\sqrt{5}-9y\sqrt{5}=12\sqrt{5}. Since there’s a \sqrt{5} in every term, you can just divide the whole equation by \sqrt{5} to eliminate the darn things! The equation simplifies to 2x-9y=12.

From there, this is a pretty easy problem. Solve for x by elimination:


From there, continue to solve for y:


The question asks you for the sum of the coordinates of the ordered pair that satisfies the system of equations, so you have to add:


Gridding in either the fraction or the repeating decimal is fine as long as you fill all the boxes with the decimal (i.e., you enter “1.11”).