Question

Form the simultaneous linear equations using the determinants

D = `|(4, -3),(2, 5)|`, D_x = `|(5, -3),(9, 5)|`, D_y = `|(4, 5),(2, 9)|`

Answer 1

If a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are linear equations in two variables, then

D = `|("a"_1, "b"_1),("a"_2, "b"_2)|`,  D_x = `|("c"_1, "b"_1),("c"_2, "b"_2)|`, D_y = `|("a"_1, "c"_1),("a"_2, "c"_2)|`   ...(i)

Given, D = `|(4, -3),(2, 5)|`, D_x = `|(5, -3),(9, 5)|`, D_y = `|(4, 5),(2, 9)|`

Comparing these determinants with equation (i), we get

a₁ = 4, b₁ = –3, c₁ = 5

a₂ = 2, b₂ = 5, c₂ = 9

∴ The required equations are 4x – 3y = 5 and 2x + 5y = 9.