Question

Solve the following equation by Cramer’s method.

4m − 2n = –4 ; 4m + 3n = 16

Answer 1

4m – 2n = –4 Here, a₁ = 4, b₁ = –2, c₁ = –4

4m + 3n = 16 Here, a₂ = 4, b₂ = 3, c₂ = 16

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

= `|(4, -2), (4, 3)|`

= 4 × 3 –(–2) × 4

= 12 + 8

D = 20

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

= `|(-4, -2), (16, 3)|`

= (–4) × 3 –(–2) × 16

= –12 + 32

D_m = 20

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

= `|(4, -4), (4, 16)|`

= 4 × 16 –(–4) × 4

= 64 + 16

D_n = 80

By Cramer’s rule,

`m = D_m/D`

= `20/20`

m = 1

`n = D_n/D`

= `80/20`

n = 4

m = 1 and n = 4 is the solution of the given simultaneous equations.