Maths / Changing the subject of the Formula(1)

Changing the subject of the Formula

1. Remove brackets and denominators first.

2. Take the letter that is furthest away from the subject to the other side of the equal sign first.

3. Always use inverse (opposite) operations.

4. Continue removing all letters to the other side of the equal sign until the subject is on its own.

Example: make y the subject of each formula

1. b =

2. x =

3. x = +

= b

3y = 2b (inverse of dividing by 2 is multiplying by 2)

y = (inverse of multiplying by 3 is dividing by 3)

(b) x =

= x

y + 2 = 3x (inverse of dividing by 3 is multiplying by 3)

y = 3x – 2 (inverse of plus 2 is subtract 2)

(c) + = x

+ = (common denominator)

3y + 2m = 6x (cancel the 6’s from both sides)

3y = 6x- 2m (opposite of plus 2m is minus 2m)

y = (opposite of multiply by 3 is divide by 3)

Practice Questions: Make y the subject

1. 4y + x = 2

2. 3x + 2y = 17

3. 5g – 6y = ab

4. 3xy + 7 = h

5. + = 3

6. 2(y + 3x) = 7

Answers

1. 4y = 2 – x

y =

2. 2y = 17 – 3x

y =

3. - 6y = ab – 5g

y =

=

4. 3xy + 7 = h

3xy = h – 7

y =

5. + = 3

+ =

6y + 5b = 45

6y = 45 – 5b

y =

6. 2(y + 3x) = 7

2y + 6x = 7

2y = 7 – 6x

y =

Some harder examples: Make h the subject

(a) v = h

(b) y = 2

(c) s = 2 (r + h)

Answers

(a) v = h

h = v

h = 3v

h =

(b) y = 2

2 = y

=

a-h = ²

-h= ² -a

h = - ² +a

(c) s = 2 (r + h)

2 (r + h) = s

r + h =

h = – r

Take home practice questions

Solve each equation for the letter shown in brackets:

1. v = u + at (a)

2. p = r I² (I)

3. R = (y)

4. T = 2 ( )

5. y = 2x + 7 (x)

6. x = (b)

Answers

1. a =

2. I =

3.

4. = ²

5. x =

6. b =