# SAT Math: Focus on Lines & Systems of Equations

This book is the second in a series that addresses the topics that appear most frequently in the Math section of the New SAT. You’ll review the properties of lines, including their graphs, and look at the different methods for solving systems of linear equations. Then you’ll apply what you know as you solve 25 problems — some done without your calculator and some with, just as it is on test day. Each problem comes with a full explanation of how to arrive at the correct answer.

We’d like to help as many students as possible achieve success on the SAT, so we’ve made the price of each of the volumes in this series just \$0.99.

The book can be purchased on Amazon by clicking on the image to the left or going here.

# SAT Math: Systems of Equations

The new SAT has shifted the focus of the math questions away from geometry and more toward algebra and functions. One of the topics you’ll want to master is systems of linear equations. If the practice tests are any indication, you can expect to see four or five of these questions on each test.

Below you’ll find a link to 10 sample system of equations questions (and a second link to the solutions).

But first, let’s do a little review.

Most systems of linear equations have a single ordered pair as their solution. It’s the point where the two lines intersect, and you can find the coordinates of that point by graphing the lines on  your calculator or using the substitution or elimination methods. But what about the special cases? Let’s take a look at systems that have either an infinite number of solutions or no solution at all.

# SAT Math: More Systems of Equations Problems

If you’ve read my recent post on Solving Systems of Equations “Cleverly” and you’re looking to try a few more of these problems, you’ll find five more below.  Remember, although you can solve these problems the same way you did in Algebra 1, our goal is to do them in an efficient way so that we can conserve some time that can then be used to solve other problems in the section.

1)  Given the equations 3x + 8y = 24 and 2x – 13y = 26, what is the value of x – y?

(A) 8
(B) 10
(C) 12
(D) 14
(E)  16

# SAT Math: Solving Systems of Equations “Cleverly”

If you want to do well on the SAT Math test, there are certain topics (functions, right triangles involving Pythagorean Theorem, 30-60-90 and 45-45-90 triangles, problems that can be solved by plugging in numbers) that you simply must master.  If you’re looking to score exceptionally well (think 700+), then you’ll also need to be very good at the types of problems that appear less frequently but often in the latter part of a section.  These are often the problems that can be the difference between a  very good score and a great score.

One type of problem that falls into this category is the systems of equation problem.  You remember these from Algebra 1 (and probably again in Algebra 2) — multiple equations with more than one variable share a common solution that you are asked to find.  A typical problem of this type that you would have seen in math class would go something like this:

Find the solution to the system 3x – 2y = 22 and 7x + 2y = 18.