Simplify: (i) $\left( {5x - 9y} \right) - \left( { - 7x + y} \right)$
(ii) $\left( {7 - 2x + 5y} \right) - (x - y) - (5x + 3y - 7)$

Hint: The above problem is based on the addition and subtraction of the values which have the same variable and separate the different variables.
Variables are the values whose numerical value keeps on changing such as x and y.
Using the above mentioned concept we will solve the given two expressions.

Complete step-by-step answer:
Let us first discuss how we must do the calculation for solving the given expression.
In the given expressions if we come across the term which has the same variable but different coefficient, then we will add or subtract the term having the same variable.
(i) $\left( {5x - 9y} \right) - \left( { - 7x + y} \right)$
$ \Rightarrow 5x - 9y + 7x - y$ (terms which the same variable but different coefficient will be added)
$ \Rightarrow 12x - 10y$ (terms having positive value will be added and the terms having negative values wll also be added but with negative sign)
12x -10y is the final expression of the first expression given in the question.
(ii) $\left( {7 - 2x + 5y} \right) - (x - y) - (5x + 3y - 7)$
$ \Rightarrow 7 - 2x + 5y - x + y - 5x - 3y + 7$ (we have opened the bracket by considering the negative sign in mind before the bracket)
$ \Rightarrow - 8x + 3y$ (we have cancelled the common terms because one was positive and one was negative and added the terms with variables according to the signs they have)

-8+3y is the final expression of the second part of the question.

Note:
The expression which was given to us in the question is a polynomial because the expression contains more than two terms, the expression which contains only one term is a monomial, expression which contains two terms is called binomial and the expressions with three terms is called trinomial. Name of the expression depends on the term it contains.