Question

Solve the following systems of linear equations by Cramer’s rule: 

(i) 5x – 2y + 16 = 0, x + 3y – 7 = 0 

(ii) (3/x) + 2y = 12, (2/x) + 3y = 13

(iii) 3x + 3y – z = 11, 2x – y + 2z = 9, 4x + 3y + 2z = 25

(iv) (3/x) - (4/y) - (2/z) - 1 = 0, (1/x) + (2/y) + (1/z) - 2 = 0, (2/x) - (5/y) - (4/z) + 1 = 0 

Answer 1

(i) 5x – 2y + 16 = 0, x + 3y – 7 = 0 

The above equations are 5x – 2y = -16 and x + 3y = -7

The matrix form of two above equations is

Now,

(iii) 3x + 3y – z = 11, 2x – y + 2z = 9, 4x + 3y + 2z = 25

The matrix form

x = 2; y = 3; z = 4

(iv) 

The above equations become

3a - 4b - 2c = 1

a + 2b + c = 2

2a - 5b - 4c = - 1

The matrix form of the above equations is

Here