Question

Solve the following system of equations by using the method of cross multiplication:

7x – 2y = 3, 22x – 3y = 16

Answer 1

7x – 2y – 3 = 0   ...(1)

22x – 3y – 16 = 0   ...(2)

From equation (1): a₁ = 7, b₁ = –2 and c₁ = –3

From equation (2): a₂ = 22, b₂ = –3 and c₂ = –16

Using cross multiplication method:

`x/(32 - 9) = y/(-66 + 112) = 1/(-21 + 44)`

`x/23 = y/46 = 1/23`

`x/23 = 1/23`

⇒ `x = 23/23`

⇒ x = 1

And `y/46 = 1/23`

⇒ `y = 46/23`

⇒ y = 2