Paper 4: Fundamentals of Business Mathematics & Statistic

2.52 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

SOLVED EXAMPLES

Example 87 : Solve 4x + 2y – 15 = 5y – 3x + 16 ... (1)

5x – y – 30 = 4 (y – x) + 11 ... (2)

Solution :

From (1), 4x + 2y – 15 – 5y + 3x – 16 = 0

Or, 7x – 3y = 31 ................... (3)

From (2) (in the same way)

9x – 5y = 41 .................. ..... (4)

Multiplying (3) by 5 and (4) by 3, we find

35x – 15y = 155

27x – 15y = 123

Substracting. 8x = 32 or, x = 4

Now putting x = 4 in eqn. (3)

7.4 – 3y = 31 or, – 3y = 31 – 28 = 3 or, y = – 1.

Example 88 : Solve x4 5+y=^22 .... (1)

x y 23

5 4+ = .... (2)

Solution :

From (1), 5x 4y 20 + =^22 or, 5x + 4y = 440 ... (3)

From (2), 4x 5y 20 + =^23 or, 4x + 5y = 460 ... (4)

Multiplying (3) by 4 and (4) by 5 and then substracting we get – 9y = – 540 or, y = 60.

Putting this value of y in (3), we find x = 40.

2.7.1. QUADRATIC EQUATION

An equation in which the highest power of x (unknown) is two is called an equation of second degree or

quadratic.

Thus, x^2 – 5x + 6 = 0, x^2 – 9x = 0, x^2 = 0 are all quadratic equations.

ax^2 + bx + c = 0, (a ≠ 0) is a standard form of quadratic equation. If b = 0 equation is pure quadratic. If

b ≠ 0 the equation is adfected quadratic.

Methods of solution

There are two methods of solution as follows :

(a) by factorisation, and

(b) by completing the square.

In the case of (a), we are to break middle term and hence to form two factors.