S2 - NT 54 Change Subject of a Formula, Find Value of Unknown Quantity

Changing the subject of a Formula/Equation

Y in term of X => to make Y the subject in relation to X and other numerical.

=> y = ?

Example  Express y in term of x for 2y - 3x = 0 

=> making the equation into y =  ?x + ?

                     L.H.S    R.H.S.            [ L.H.S:Left Hand Side/R = Right]

                2y - 3x = 0

Step 1: Only y (the subject) on the L.H.S

           'shift' other variables/numbers to the R.H.S

  

           + 3x to both side to 'cancel'/'remove' from L.H.S to R.H.S

              +3x  2y - 3x = 3x

               2y = 3x

<< We add + 3x to both side for the equation to remain the 'same' >>

Step 2 : Making the equation 'y = ? 

              'reduce' 2y to y by dividing 2 (or x 1/2)  to both side of the equation

½ x 2y = ½ x 3x

        y = 3x

        2

 

     =>   'Shift' = 

             .  bring variable/number to the other side of = , 

             .  change its sign

                  Negative(-) bring over = Positive (+) at the other side of = 

                  Positive(+) bring over = Negative (-) at the other side of =

Example

Given that y = 2x - 7, make x the subject.

<< to make t the subject, 'move' x to L.H.S>>

2x - 7 = y ( a = b => b = a)

     2x = y + 7      (Step 1: Place -7 to the RHS => +7)

       x = y + 7      (Step 2 : Change to 'x = ' , /2 for both side)

                      2

Example

Express y in term of x

            3x + 2 = 4 - 2y

                   

            3x + 2y = 4 – 2.                   (Step 1: Place +y to the LHS)

                    2y = 2 – 3x                  (Step 2 : 'shift' 3x to R.H.S => -3x at R.H.S)

                      y = 2/2 – 3x/2.           (Step 2 : Change to 'y = ' , /2 for both side)

                      y = 1 – 3x/2

<< Level 2 - More challenging example >>

Example

Express ⅓y + 2 = 4 - 5x

                ⅓y = 4 - 5x - 2 (Step 1 : 'shift' +2 to R.H.S => -2 at R.H.S)

                   ⅓ y = 2 - 5x (Step 2 : Change to 'y = ' , x 3 for both side)

              3 x ⅓y = 3 (2 - 5x)

                       y = 3(2 - 5x)      

 Note: when x or / for both side, it applies to the entire 'string' of expression

  => 3 x (2 - 5x) and NOT  3 x 2 + 5x

Finding the Variable's Quantity (Unknown Quantity)

In an equation, the quantity of the variables changes with different given values of the other variable. Thus, the variable's quantity can be found when the quantity/value of the other variable is given. 

Example

a. Make q the subject of 4p + 2q = 5. 

b. What is the value of y when (i) p = 3 and (ii) p = 5

a. 4p + 2q = 5                    (Step 1 : 'shift' 4x to R.H.S => -4x at R.H.S)

        2q = 5 - 4p 

          q = ½ (5 - 4p)       (Step 2 : Change to 'q = ' , x ½ for both side)

b(i).    When p = 3

  << Substitute/put the value of p into the equation  >>

       q = ½ (5 - 4(3)).  

                  = ½ (5 - 12)

          = ½ x -7

                  = 3½

Example

a. Make t the subject of v = u + at. 

<< to make t the subject, 'move' t to L.H.S>>

 v = u + at

  u + at = v (Step 0: Rule : a = b => b = a, move subject to LHS))

  at = v - u (Step 1 : 'shift' u to R.H.S => -u at R.H.S)

  t = v - u       (Step 2 : Change to 't = ' , ÷ a for both side)

                                           a

b.  What is the value of t when v = 8, u = 2 and a = 3?

  t = v - u 

          a

  t = 8 - 2

  3

    = 6/3 = 2

Practice

1.  Make p the subject of the formula 2p + 2 = q

2.  Make q the subject of the formula 6q - 5p = 1

3.  Make q the subject of the formula 2p + 2 = 4q - p

4.   Make q the subject of the the formula 3q - 1 = 2p + 5. 

      What is the value of q when (i) p = 1, (ii) p = 4

5.           F = m(v - u)

                       t  

Calculate the value of F when m = 40, v = 35, u = 23 and t = 8 (S12/II/5)

6.  Given that y = 2x - 7, make x the subject. (S11/I/3)