Question

Solve the following systems of equations using matrix method. 

2x + 8y + 5z = 5; 

x + y + z = - 2; 

x + 2y - z = 2.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

2x + 8y + 5z = 5; 

x + y + z = - 2; 

x + 2y - z = 2 

Converting the following equations in matrix form, 

AX = B

2R₂ – R₁ 

2R₃ – R₁

Again converting into equations, we get 

2x + 8y + 5z = 5 

- 6y - 3z = - 9 

- 15z = 15 

Z = - 1 

- 6y - 3 × - 1 = - 9 

- 6y = - 9 - 3 

Y = 2 

2x + 8×2 + 5× - 1 = 5 

2x = 5 - 16 + 5

x = - 3

∴ x = - 3, y = 2, z = -1