**Given : - **

Steel requirement for each car is given

Let, Number of cars produced by steel type C_{1}, C_{2} and C_{3} be x, y and z respectively.

**Now, **

We can arrange this model in linear equation system

**Thus, **

We have

2x + 3y + 4z = 29

x + y + 2z = 13

3x + 2y + z = 16

**Here,**

**Solving determinant,**

expanding along 3^{rd} column

⇒ D = 1[30 – 25]

⇒ D = 5

⇒ D = 5

**Again, **

Solve D_{1} formed by replacing 1^{st} column by B matrices

**Here,**

**Solving determinant,**

expanding along 3^{rd} column

⇒ D_{1} = 1[( – 35)( – 3) – ( – 5)( – 19)]

⇒ D_{1} = 1[105 – 95]

⇒ D_{1} = 10

**Again, **

Solve D_{2} formed by replacing 2^{nd} column by B matrices

**Here,**

**Solving determinant,**

expanding along 3^{rd} column

⇒ D_{2} = 1[190 – 175]

⇒ D_{2} = 15

**And, **

Solve D_{3} formed by replacing 3rd column by B matrices

**Here,**

**Solving determinant, **

expanding along 1^{st} column

⇒ D_{3} = – 1[ – 23 – ( – 1)3]

⇒ D_{3} = 20

**Thus by Cramer’s Rule, we have**

**Thus,**

Number of cars produced by type C_{1}, C_{2} and C_{3} are 2, 3 and 4 respectively.