Question

निम्नलिखित युगपत समीकरणों को क्रेमर की पद्धति से हल कीजिए।

3x − 2y = `5/2`; `1/3`x + 3y = `-4/3`

Answer 1

3x − 2y = `5/2` ........(I)

`1/3`x + 3y = `-4/3` .........(II)

यहाँ, a₁ = 3, b₁ = − 2, c₁ = `5/2` तथा

a₂ = `1/3`, b₂ = 3, c₂ = `-4/3`

D = `|("a"_1, "b"_1), ("a"_2, "b"_2)| = |(3, -2), (1/3, 3)|`

= (3 × 3) − `(−2 × 1/3)`

= `9 + 2/3`

= `(27 + 2)/3`

= `29/3`

D_x = `|("c"_1, "b"_1), ("c"_2, "b"_2)| = |(5/2, - 2), (-4/3, 3)|`

= `(5/2 xx 3) - [(-2) xx (-4/3)]`

= `15/2 - 8/3`

= `(45 - 16)/6`

= `29/6`

D_y = `|("a"_1, "c"_1), ("a"_2, "c"_2)| = |(3, 5/2), (1/3, -4/3)|`

= `(3 xx -4/3) - (5/2 xx 1/3)`

= `-4 - 5/6`

= `(-24 - 5)/6`

= `-29/6`

क्रेमर की पद्धति के अनुसार,

x = `"D"_"x"/"D" = ((29/6))/((29/3)) = 29/6 xx 3/29 = 3/6 = 1/2`

y = `"D"_"y"/"D" = (((-29)/6))/((29/3)) = -29/6 xx 3/29 = (-3)/6 = -1/2`

∴ दिए गए समीकरणों का हल (x, y) = `(1/2, -1/2)` है।