Question

Solve the following simultaneous equations using Cramer's rule:

4m + 6n = 54; 3m + 2n = 28

Answer 1

The given simultaneous equations are

4m + 6n = 54                        ...(i)
3m + 2n = 28                        ...(ii)

Comparing the given equation with

a₁m + b₁n = c₁ and a₂m + b₂n = c_2, we get

a₁ = 4, b₁ = 6, C₁ = 54
a₂ = 3, b₂ = 2, c₂ = 28

       `D = |(a_1, b_1),(a_2, b_2)| = |(4,6),(3,2)| = 8 -18 = - 10`

 

     `Dm = |(c_1, b_1),(c_2, b_2)| = |(54,6),(28,2)| = 108 - 168 = -  60 `

 

    `Dn = |(a_1, c_1),(a_2, c_2)| = |(4,54),(3,28)| = 112 - 162 = - 50`

∴ By Cramer's rule, we get

                                `m = D_m/D = (-60)/-10 = 6`

and                          `n = D_n/D = (-50)/-10 = 5`

  ∴  Solution = (m, n) = (65)