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# Cramer‚Äôs Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems

Business Maths and Statistics : Applications of Matrices and Determinants: Cramer‚Äôs Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems with Answers, Solution and Explanation

## Cramer‚Äôs Rule (Non Homogeneous linear equations upto three variables): Solved Example Problems

Example 1.19

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer‚Äôs rule.

Solution:

The equations are

2x + 3y = 7

3x + 5y = 9

Here ‚à¥ we can apply Cramer‚Äôs Rule ‚à¥ By Cramer‚Äôs rule ‚à¥    Solution is      = 8, y = ‚àí3

Example 1.20

The following table represents the number of shares of two companies A and B during the month of January and February and it also gives the amount in rupees invested by Ravi during these two months for the purchase of shares of two companies. Find the the price per share of A and Bpurchased during both the months Solution:

Let the price of one share of A be x

Let the price of one share of B be y

‚à¥ By given data, we get the following equations

10x + 5y = 125

9x + 12 y = 150 ‚à¥ By Cramer‚Äôs rule The price of the share A is ‚Çπ10 and the price of the share B is ‚Çπ5.

Example 1.21

The total cost of 11 pencils and 3 erasers is ‚Çπ 64 and the total cost of 8 pencils and 3 erasers is ‚Çπ49. Find the cost of each pencil and each eraser by Cramer‚Äôs rule.

Solution:

Let ‚Äòx‚Äô be the cost of a pencil

Let ‚Äòy‚Äô be the cost of an eraser

‚à¥ By given data, we get the following equations

11x + 3y =64

8x+3y=49 ‚à¥ The cost of a pencil is ‚Çπ 5 and the cost of an eraser is ‚Çπ 3.

Example 1.22

Solve by Cramer‚Äôs rule x + y + z = 4, 2x ‚àí y + 3z = 1, 3x + 2 y ‚àí z = 1

Solution: ‚à¥ We can apply Cramer‚Äôs Rule and the system is consistent and it has unique solution. The solution is     ( x , y, z) = ( ‚àí1,3, 2)

Example 1.23

The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is ‚Çπ840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is ‚Çπ570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is ‚Çπ630. Find the cost of each book by using Cramer‚Äôs rule.

Solution:

Let ‚Äòx‚Äô be the cost of a Business Mathematics book

Let ‚Äòy‚Äô be the cost of a Accountancy book.

Let ‚Äòz‚Äô be the cost of a Commerce book.

‚à¥ 3x + 2 y + z = 840

2x + y + z = 570

+ y + 2= 630 ‚à¥ The cost of a Business Mathematics book is ‚Çπ120,

the cost of a Accountancy book is ‚Çπ150 and

the cost of a Commerce book is ‚Çπ180.

Example 1.24

An automobile company uses three types of Steel S1S 2 and S3 for providing three different types of Cars C1C2 and C3. Steel requirement R (in tonnes) for each type of car and total available steel of all the three types are summarized in the following table. Determine the number of Cars of each type which can be produced by Cramer‚Äôs rule.

Solution:

Let ‚Äòx‚Äô be the number of cars of type C1

Let ‚Äòy‚Äô be the number of cars of type C2

Let ‚Äòz‚Äô be the number of cars of type C3

3x + 2 y + 4z = 28

+ y + 2= 13

2x + 2 y + z = 14 ‚à¥ The number of cars of each type which can be produced are 2, 3 and 4.

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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Cramer‚Äôs Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems |