SUBSTITUTION –
The process of replacing the variables in an expression by numbers is called ‘Substitution’. The value thus obtained is called the value of the expression for those values of the variables.
Substitution in a Formula –
To find the value of an unknown variable from the formula when the values of the other variables are given, we should take the following steps –
Step.1) First we should make the unknown variables the subject of the formula.
Step.2) Substitute the values of the known variables in the formula and find the value of the unknown variable.
Example.1) If, x = 2, y = -5, z = -3, then the find the value of x² - 2yᶟz + 3xy²+ 5yz²
Ans.) Substituting the given values of x, y, & z in the given expression -
x² - 2yᶟz + 3xy² + 5yz²
= 2² - 2. (-5)ᶟ.(-3) + 3.2.(-5)² + 5.(-5).(-3)²
= 4 – (-).(-).(-).(-).(2 X 5 X 5 X 5 X 3) + (-).(-).(3 X 2 X 5 X 5) + (-).(-).(-).(5 X 5 X 3 X 3)
= 4 – 750 + 150 – 225 = - 821 (Ans.)
Example.2) If, x = 3, y = 5, z = 4, then the find the value of 4x⁴y²- 3yz²- 5xy²- 2y²z
Ans.) Substituting the given values of x, y, & z in the given expression -
4x⁴y² - 3yz² - 5xy² - 2y²z
= 4 X (3 X 3 X 3 X 3) X (5 X 5) – 3 X 5 X (4 X 4) – 5 X 3 X (5 X 5) – 2 X (5 X 5) X 4
= 8100 – 240 – 375 – 200 = 8100 – 815 = 7285 (Ans.)