Equations with 3 or 4 variables appear frequently in the last part of Math sections on the SAT. Do not get scared or confused by the vast number of variables, but instead approach these equations exactly as you would an equation that contains only one variable.

TIP FOR EQUATIONS WITH 3 OR 4 VARIABLES
When faced with these questions, make sure to first identify the final form of your answer. This form will not only determine the easiest way to manipulate and solve the equation but it will also ensure that you don’t get confused by the multiple variables in the problem.

     Example: If w - 7(d + 3) = p, what is the value of w in terms of d and p?
     The Final Form of Your Answer: w = ?dp

SAMPLE PRACTICE QUESTIONS FOR EQUATIONS WITH 3 OR 4 VARIABLES

1. If js + j^-1 = k - 2s + j / k , what is the value of s when j = 2 and k = .5?

     Solution
     js + j^-1 = k - 2s + j / k --> 2s +2^-1 = .5 - 2s + 2/.5 --> 2s +1/2 = .5 - 2s + 4 --> 4s + 1/2 = 4.5 --> 4s = 4 --> s = 1

2. If x = 4p^1/2 and z^-1/2 = 2n^-1/4, what is the value of (xz)² in terms of p and n?

     Solution (The equation must be manipulted to the terms x² = ? and z² = ?)
     1) x = 4p^1/2 --> x⁽¹⁾⁽²⁾ = 4p^(1/2)(2/1) --> x² = 4p
     2) z^-1/2 = 2n^-1/4 --> z^(-1/2)(-4/1) = 2n^(-1/4)(-4/1) --> z² = 2n
     3) x²z² = (xz)²
     4) (xz)² = (4p)(2n)
     5) (xz)² = 8pn

SAT MATH: Equations with 3 or 4 Variables

Lesson Includes:

—Approaches to Math Equations

—Tip for Math Equations with 3 or 4 Variables

—Sample Practice Questions

—Practice Questions

Math

SAT Reading

SAT Writing

SAT Vocabulary

EQUATIONS REVIEW QUIZ

This SAT Math Quiz provided for you by: