S.A.T. Math Testing Tactics

Tactic 17: Add Equations

When a question involves two or more equations, try adding the equations together.

Many questions involving systems of equations have a solution shortcut that may only become apparent after the equations have been combined.

Example 17.1 If 3x + 5y = 14 and x – y = 6, what is the

average of x and y?

What is the question asking for?

2

yxaverage

Instead of solving by traditional substitution or elimination methods, try adding the two equations…

Example 17.1 (continued) If 3x + 5y = 14 and x – y = 6, what is the

average of x and y?

3 5 14x y 6 yx+

2044 yx

5

4

yx

2

yxaverage

5.22

5average

If A+B = 1, B –C = 2, and C – A = D, what is D in terms of B?

Example 17.2

DAC

CB

BA

2

1

+

DB 32DB

DB

32

3 3

32

If A – B + C = 7 and A + B – C = 11,which of the following must be true?

I.) A is positive II.) B > C III.) BC < 0

Example 17.3

11

7

CBA

CBA+

9

182

A

A

So I. is true… A is positive

Let’s check II. and III. by substitutingA=9 into the original equations.

Example 17.3 (continued)

2

)2(1

2

79

7

CB

CB

CB

CB

CBA

If B=5 and C=3, this new statement is true.

II. B > C TRUE!!! 5>3

III. BC<0 FALSE!!! 5x3>0

I. and II. must be true

If you are solving a problem on the SAT that deals with two or more equations, try adding the equations together.

The resulting sum may help you see a shortcut to solving the

problem!

In conclusion: