Application of Determinants - Cramer’s Rule

Solve the following equations by using Cramer’s rule:

2x + 3y = 7; 3x + 5y = 9

Solve the following equations by using Cramer’s rule:

5x + 3v = 17; 3x + 7y = 31

Solve the following equations by using Cramer’s rule:

2x + y – z = 3, x + y + z – 1, x – 2y – 3z = 4

Solve the following equations by using Cramer’s rule:

x + y + z = 6, 2x + 3y – z = 5, 6x – 2y – 3z = – 7

Solve the following equations by using Cramer’s rule:

x + 4y + 3z = 2, 2x – 6y + 6z = – 3, 5x – 2y + 3z = – 5

A commodity was produced by using 3 units of labour and 2 units of capital, the total cost is ₹ 62. If the commodity had been produced by using 4 units of labour and one unit of capital, the cost is ₹ 56. What is the cost per unit of labour and capital? (Use determinant method)

A total of ₹ 8,600 was invested in two accounts. One account earned `4 3/4`% annual interest and the other earned `6 1/2`% annual interest. If the total interest for one year was ₹ 431.25, how much was invested in each account? (Use determinant method)

At marina two types of games viz., Horse riding and Quad Bikes riding are available on hourly rent. Keren and Benita spent ₹ 780 and ₹ 560 during the month of May.

Find the hourly charges for the two games (rides). (Use determinant method)