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निम्नलिखित युगपत समीकरणों को क्रेमर की पद्धति से हल कीजिए। 3x − 2y = 52; 13x + 3y = -43 - Mathematics 1 - Algebra [गणित १ - बीजगणित]

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Sum

निम्नलिखित युगपत समीकरणों को क्रेमर की पद्धति से हल कीजिए।

3x − 2y = `5/2`; `1/3`x + 3y = `-4/3`

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Solution

3x − 2y = `5/2` ........(I)

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

यहाँ, a1 = 3, b= − 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`

Dx = `|("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`

Dy = `|("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।

Concept: निशच्यक पद्धति (क्रेमर की पद्धति) Determinant Method (Crammer’s Method)
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Balbharati गणित १ १० वीं कक्षा Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board | Hindi Medium
Chapter 1 दो चरांकों वाले रेखीय समीकरण
प्रकीर्ण प्रश्नसंग्रह 1 | Q 5. (3) | Page 28
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