Question

Solve the following systems of equations using matrix method. 

4x + 3y + 2z = 60; 

x + 2y + 3z = 45; 

6x + 2y + 3z = 70.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

4x + 3y + 2z = 60 

x + 2y + 3z = 45 

6x + 2y + 3z = 70 

Converting the following equations in matrix form, 

AX = B

4R² – R₁ 

2R₃ – 3R₁

Again converting into equations, we get 

4x + 3y + 2z = 60 

5y + 10z = 120 

- 5y = - 40 

y = 8 

5 × 8 + 10z = 120 

10z = 120 - 40 

10z = 80 

z = 8 

4x + 3×8 + 2×8 = 60 

4x = 60 – 24 - 16 

4x = 20 

x = 5 

∴ x = 5 , y = 8 , z = 8