1. Tactic 17: Add Equations

2. 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.

3.  If 3x + 5y = 14 and x – y = 6, what is the average of x and y?  What is the question asking for? Instead of solving by traditional substitution or elimination methods, try adding the two equations…

4.  If 3x + 5y = 14 and x – y = 6, what is the average of x and y? +

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

6.  If A – B + C = 7 and A + B – C = 11, which of the following must be true? I.) A is positiveII.) B > CIII.) BC < 0 + So I. is true… A is positive Let’s check II. and III. by substituting A=9 into the original equations.

7. If B=5 and C=3, this new statement is true. II. B > CTRUE!!! 5>3 III. BC<0 FALSE!!! 5x3>0 I. and II. must be true

8.  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!