Some SAT Algebra questions will not only have one variable, but two or three for you to keep in mind. On occasion you’ll be given a set of equations, a “system” of equations, and asked to solve for one or all of the many variables in that system. You will also encounter questions like these that will give you a fifth option, choice E: This question cannot be solved with the information given. Remember this general rule of thumb: you must have the SAME NUMBER of equations as unknowns. If there are three variables and only two equations provided, chances are you will not be able to solve the problem. If there are two variables AND two equations given, chances are you will be able to solve it.

However, the SAT has a few tricks up its sleeve—here are two of the most common ones:

2x-y=14, and 4x-2y=28.

Two equations, two variables—should be simple, right? Let’s try our first tactic, substitution, and see what happens. Solve the first equation for y, and we get 2x-14=y. Fantastic—plug that expression in for y in the second equation. 4x-2(2x-14)=28. Distribute: 4x-4x+28=28. Reverse PEMDAS, and we’re left with… 0=0.

Well, while 0=0 is certainly true, it isn’t very helpful! Where was the trick? 2x-y=14 and 4x-2y=28 are the same equation. The second is simply the first multiplied by two. None of the relationships have changed between the variables and thus no new information is provided. This is really a two-variable, one-equation problem—it can’t be solved with the information provided.
Here’s a second trick, one that may make you give up before you even examine the numbers.

2m+z+5p=10, and 2m-z+3p=6. Find the value of p.

Shoot, only two equations, but three variables; it must be unsolvable… Let’s try another technique before we write this one off and move on. This problem requires a little bit of heavy lifting in the world of systems of equations: linear combination (combining multiple equations by either addition, subtraction, multiplication or division in order to cancel out variables). In this case, subtract the second equation from the first (setting up the problem vertically):

2m+z+5p=10
+ 2m-z+3p=6
0 + 0 +8p = 16 becomes 8p=16. Divide both sides by 8, and p=2.

Using linear combination, you were able to cancel out two variables, leaving you with 8p=16, a one-variable, one-equation problem!

QUICK TIP: Use the general rule of thumb that you must have the same number of equations as unknowns, but keep in mind the two ways the SAT can disguise these problems!

Sarah Fine, an advisor to Lumina Prep, recently published a column on the coverage that education receives in the media. Specifically, Sarah focuses on the topics that seem to get coverage versus those that go largely unreported.

Those interested in the larger topic of Education can read Sarah’s article here:

http://blog.ednewscolorado.org/2010/01/12/write-like-your-school-is-on-fire/

Some of our readers may know of our work with African Leadership Academy in South Africa. We were excited to see one of its students interviewed on The Daily Show with Jon Stewart the other night and we felt compelled to share the remarkable story of William Kamkwamba, who at the age of 14 built a windmill for his village in Malawi. You can read more on his website at http://williamkamkwamba.typepad.com/williamkamkwamba/ or just watch the interview in the video below.

Although he mentioned studying for the SAT, he surely doesn’t need the help. In any case, Lumina Prep is honored to be part of the story thorough our affiliations with African Leadership Academy.

About African Leadership Academy:
African Leadership Academy (ALA) is an elite, residential secondary institution located on the outskirts of Johannesburg, South Africa for outstanding 15-18 year old youth from all 54 African nations and around the world. ALA was founded in 2004 by Fred Swaniker, Chris Bradford, Peter Mombaur, and Acha Leke with the mission to “transform Africa by developing and supporting future generations of African leaders—ethical and innovative leaders who will usher the continent into a peaceful and prosperous future. To achieve this goal, ALA teaches a unique two- year curriculum in African studies, leadership and entrepreneurship as well as the usual academic core subjects. ALA officially opened in September 2008 with an inaugural class of 97 students from 29 countries worldwide.