Question

For the equations y + 2x = 19 and 2x – 3y = − 3, find the value of D.

Answer 1

The given equations are

y + 2x = 19

i.e., 2x + y = 19

2x – 3y = – 3

Comparing the given equations with a₁x + b₁y = c₁ and a₂x + b₂y = c₂,

we get

a₁ = 2, b₁ = 1, c₁ = 19

a₂ = 2, b₂ = – 3, c₂ = – 3

∴ D = `|("a"_1, "b"_1),("a"_2, "b"_2)|`

= `|(2, 1),(2, -3)|`

= 2 × (– 3) – 1 × 2

= – 6 – 2

= – 8