Hard System of Equations Question with Solution

Hard System of Equations Problem for the Revised SAT

Last week I gave you a Level 5 problem about systems of equations for the revised SAT to try. Today I will provide a solution. If you have not yet attempted the problem go back and take a look at it first so you can try it on your own. Here is the link: Hard Problem for the Revised SAT

Level 5 – System of Equations

Here is the problem once again followed by solutions:

3x + 9y = 11
cx + dy = 55

In the system of equations above, c and d are constants. If the system has infinitely many solutions, what is the value of c/d ?

Solution: The system of equations

3x + 9y = 11
cx + dy = 55

has infinitely many solutions if 3/c = 9/d = 11/55. In particular, we must have 3/c = 9/d, or equivalently c/d = 3/9 = 1/3 or .333.

Note: The general form of an equation of a line is ax + by = c where a, b, and c are real numbers. More information about this type of equation can be found in the books below.

Feel free to add your own solutions to the comments.

More Hard SAT Math Practice Problems

For many more SAT math problems like these, each with several fully explained solutions, check out my SAT math books for the revised SAT. If you received above a 600 on the PSAT take a look at

28 New SAT Math Lessons to Improve Your Score in One Month.

Everyone else should consider

New SAT Math Problems arranged by Topic and Difficulty Level.

Click on the pictures below for more information about these books.