Theory question 102
Algebraic Expressions(a) Make q the subject of the relation t = √(pq/r − r2q).
(b) If 9(1−x) = 27y and x − y = −1½, find the value of x + y.
Show the model answer
Model answer
(a) Square: t2 = pq/r − r2q. Multiply by r: rt2 = pq − r3q = q(p − r3).
q = rt2/(p − r3).
(b) 32(1 − x) = 33y, so 2 − 2x = 3y, i.e. 2x + 3y = 2.
x − y = −3/2 gives 2x − 2y = −3. Subtracting: 5y = 5, y = 1, then x = −½.
x + y = ½.
Explanation
Write 9 and 27 as powers of 3.