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Business Maths and Statistics : Applications of Matrices and Determinants: Cramerâ€™s Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems with Answers, Solution and Explanation

Example 1.19

Solve the equations 2*x* + 3*y* = 7, 3*x* + 5*y* = 9 by Cramerâ€™s rule.

*Solution:*

The equations are

2*x* + 3*y* = 7

3*x* + 5*y* = 9

Here

âˆ´ we can apply Cramerâ€™s Rule

âˆ´ By Cramerâ€™s rule

âˆ´ Solution is *x *=* *8,* y *= âˆ’3

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 *B*purchased 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*

âˆ´ By given data, we get the following equations

10*x* + 5*y* = 125

9*x* + 12 *y* = 150

âˆ´ By Cramerâ€™s rule

The price of the share *A* is â‚¹10 and the price of the share *B* is â‚¹5.

Example 1.21

The total cost of 11 pencils and 3 erasers is â‚¹ 64 and the total cost of 8 pencils and 3 erasers is â‚¹49. Find the cost of each pencil and each eraser by Cramerâ€™s rule.

*Solution:*

Let â€˜*x*â€™ be the cost of a pencil

Let â€˜*y*â€™ be the cost of an eraser

âˆ´ By given data, we get the following equations

11x + 3y =64

8x+3y=49

âˆ´ The cost of a pencil is â‚¹ 5 and the cost of an eraser is â‚¹ 3.

Example 1.22

Solve by Cramerâ€™s rule *x* + *y* + *z* = 4, 2*x* âˆ’ *y* + 3*z* = 1, 3*x* + 2 *y* âˆ’ *z* = 1

*Solution:*

âˆ´ We can apply Cramerâ€™s Rule and the system is consistent and it has unique solution.

The solution is ( x , y, z) = ( âˆ’1,3, 2)

Example 1.23

The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is â‚¹840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is â‚¹570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is â‚¹630. Find the cost of each book by using Cramerâ€™s rule.

*Solution:*

Let â€˜*x*â€™ be the cost of a Business Mathematics book

Let â€˜*y*â€™ be the cost of a Accountancy book.

Let â€˜*z*â€™ be the cost of a Commerce book.

âˆ´ 3*x* + 2 *y* + *z* = 840

2*x* + *y* + *z* = 570

*x *+* y *+* *2*z *=* *630

âˆ´ The cost of a Business Mathematics book is â‚¹120,

the cost of a Accountancy book is â‚¹150 and

the cost of a Commerce book is â‚¹180.

Example 1.24

An automobile company uses three types of Steel *S*1, *S* 2 and *S*3 for providing three different types of Cars *C*1, *C*2 and *C*3. 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 Cramerâ€™s rule.

*Solution:*

Let â€˜*x*â€™ be the number of cars of type *C*1

Let â€˜*y*â€™ be the number of cars of type *C*2

Let â€˜*z*â€™ be the number of cars of type *C*3

3*x* + 2 *y* + 4*z* = 28

*x *+* y *+* *2*z *=* *13

2*x* + 2 *y* + *z* = 14

âˆ´ 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 : Cramerâ€™s Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems |

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