Question

Solve the following simultaneous equations using Cramer’s rule.

3x – 4y = 10 ; 4x + 3y = 5

Answer 1

Given equations,

3x − 4y = 10   ...(1)
4x + 3y = 5   ...(2)

a₁ = 3, a₂ = 4, b₁ = −4, b₂ = 3, c₁ = 10, c₂ = 5

`D = |(a_1, b_1), (a_2, b_2)|`

`D = |(3, -4), (4, 3)|`

= 3 × 3 − (– 4) × 4

= 9 + 16

= 25

`D_x = |(c_1, b_1), (c_2, b_2)|`

`D_x = |(10, -4), (5, 3)|`

= 10 × 3 − (−4) × 5

= 30 + 20

= 50

`D_y = |(a_1, c_1), (a_2, c_2)|`

`D_y = |(3, 10), (4, 5)|`

= 3 × 5 − 4 × 10

= 15 − 40

= −25

By using cramer's rule,

`x = D_x/D`

= `50/25`

= 2

`y = D_y/D`

= `(-25)/25`

= −1

(x, y) = (2, −1) is the solution of the given simultaneous equation.