Changing the Subject in an Equation or Formula | How to Change the Subject in an Equation or Formula?

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Procedure for Changing Subject in an Equation or Formula?

Changing the Subject in an Equation or Formula is the way of changing the subject of formula and method of substitution to find the value of one variable. The method of substitution is the process of substituting the given values in the place of variables to find the value of the algebraic expression.

• Find the required variable as the subject.
• Note down the given values and substitutes them in the concern variables.
• Finally, simplify the expressions and find the value of the subject.

Solved Examples on Changing the Subject in an Equation or Formula

1. Make s the subject of the below Adding and Subtracting formula
(i) t = s + r
(ii) t = s – r

Solution:
(i) Given that t = s + r
Subtract r on both sides
t – r = s+r-r

t-r = s
The final answer is s = t – r
(ii) Given that t = s – r
Add r on both sides
t + r = s-r+r
The final answer is s = t +r

2. (i) Given x = ty Make y as the subject.
(ii) Given p = rq Make r as the subject.

Solution:
(i)Given that x = ty
t is multiplying y.
Divide t on both sides to get y as the subject.
x/t = y

The final answer is y = x/t

(ii) Given that p = rq
q is multiplying r.
Divide q on both sides to get r as the subject.
p/q = r

The final answer is r = p/q

3. Given B = Q {1 + (t/100)}ⁿ make t as the subject.
Given B = 1102.50 Q = 1000 n = 2, find t.

Solution:
Given that B = Q {1 + (t/100)}ⁿ
Divide Q on both sides
B/Q = Q/Q {1 + (t/100)}ⁿ
B/Q = {1 + (t/100)}ⁿ
Apply the power 1/n on both sides
(B/Q)^1/n = {1 + (t/100)}
Subtract 1 on both sides
(B/Q)^1/n – 1 = 1 – 1 + (t/100)
(B/Q)^1/n – 1 = (t/100)
Multiply 100 on both sides
100{(B/Q)^1/n – 1} = t
The answer is t = 100{(B/Q)^1/n – 1}
Substitute the given values B = 1102.50 Q = 1000 n = 2, to find t.
t = 100{(1102.50/1000)^1/2 – 1}
t = 100{(441/400)^1/2 – 1}
t = 100 [{(21/20)²}^1/2 – 1]
t = 100 [(21/20) – 1]
t = 100/20
t = 5

The final answer is t = 5.

4. Make L the subject of the following formula:
(i) s = mL + r
(ii) r = mnL + t

Solution:
(i) Given that s = mL + r
Sutract r on both sides
s – r = mL
Divide m on both sides
(s – r)/m = L

The final answer is L = (s – r)/m

(ii) Given that r = mnL + t
Sutract t on both sides
r – t = mnL
Divide mn on both sides
(r – t)/mn = L

The final answer is (r – t)/mn.

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