Question

Solve the following systems of equations using matrix method. 

6x - 9y – 20z = - 4; 

4x – 15y + 10z = - 1;

2x - 3y - 5z = - 1.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

6x - 9y - 20z = - 4 

4x – 15y + 10z = - 1 

2x - 3y - 5z = - 1 

Converting the following equations in matrix form, 

AX = B

3R₂ – 2R₁ 

3R₃ – R₁

Again converting into equations, we get 

6x - 9y - 20 z = - 4 

- 27y + 70z = 5 

5z = 1 

z = 1/5

- 27y + 70 x 1/5 = 5 

- 27y = 5 – 14 

- 27y = - 9

y = 1/3

6x - 9 x 1/3 - 20 x 1/5 = -4

6x = - 4 + 3 + 4

x = 1/2

∴ x = 1/2, y = 1/3, z = 1/5