★ Required Answer:-
First, what is an equation?
➳ A mathematical statement which shows that two algebraic expressions are equal is called and equation.
Or, LHS = RHS
Example:- 3x - 5 = x + 8
An equation is said to be a linear equation if it contains only one variable (literal) with highest power 1.
_______________________
Solving an equation:-
To solve the equation x + 5 = 7 means to find the value of an unknown algebraic quantity used in the equation.
Example:-
- To solve the equation x + 5 = 7 means to find the value of x.
- To solve the equation 3y + 2 = 9 means to find the value of y.
- To solve the equation [tex]\sf \dfrac{2a}{3} + 4 = 10[/tex] means to find the value of a ⠀⠀⠀⠀⠀⠀and so on!
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ Rules for solving an equation by the substitution method:-
Rule ❶
If x = 2, the value of the expression 3x + 2 = 3 × 2 + 2 = 6 + 2 = 8
Rule ❷
If x = 0, the value of the expression 3x + 2 = 3 × 0 + 2 = 0 + 2 = 2
Rule ❸
If x = -2, the value of the expression 3x + 2 = 3 × -2 + 2 = -6 + 2 = -4
Now consider the algebraic expression 5x - 2y
This expression consists of variables x and y.
Now if :-
- x = 3 and y = 2, 5x - 2y = 5 × 3 2 × 2 = 15 - 4 = 11
- x = 8 and y = 5, 5x - 2y = 5 × 8 - 2 × 5 = 40 - 10 = 30
⠀⠀⠀⠀⠀⠀⠀⠀
The process of finding the value of an algebraic expression by substituting the given value of its variable is called substitution.⠀⠀
