Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2

Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 दो चर वाले रैखिक समीकरण युग्म

Ex 3.2 Pair of Linear Equation in Two Variables अतिलघु उत्तरीय प्रश्न (Very Short Answer Type Questions)

निम्नलिखित रैखिक समीकरण (UPBoardSolutions.com) निकाय को हल कीजिए –

प्रश्न 1.
31x + 47y = 15, 47x + 31y = 63
हलः
समीकरण
31x + 47y = 15 …..(1)
और 47x + 31y = 63
विलोपन विधि से,
समी० (1) में 17 तथा समी० (2) को 31 से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 1
y का मान समी० (1) में रखने पर,
31x + 47 × ( – 1) = 15
31x – 47 = 15
31x = 15 + 47 (UPBoardSolutions.com)
31x = 62
x = [latex]\frac{62}{31}[/latex] ⇒ x = 2
अत: x = 2, y = – 1

UP Board Solutions

प्रश्न 2.
3x + 4y + 7 = 0, 5x – 7y – 2 = 0
हलः
समीकरण 3x + 4y + 7 = 0
3x + 4y = – 7 ….. (1)
और 5x – 7y – 2 = 0
या 5x – 7y = 2 ….. (2)
विलोपन विधि से, समी० (1) को 5 तथा समी० (2) को 3 से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 2
y = [latex]-\frac{41}{41}[/latex]
⇒ y = – 1
y का मान समी० (1) में (UPBoardSolutions.com) रखने पर,
3x + 4 × ( – 1) = – 7
3x – 4 = – 7
3x = – 7 + 4
3x = – 3
x = [latex]-\frac{3}{3}[/latex]
⇒ x = – 1
अतः x = – 1, y = – 1

UP Board Solutions

प्रश्न 3.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 3
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 4
अतः x = 1, y = 3

प्रश्न 4.
2x + 3y = 18; x – 2y = 2
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 5
y का मान समी० (2) (UPBoardSolutions.com) में रखने पर,
x – 2 × 2 = 2
x – 4 = 2
x = 2 + 4 ⇒ x = 6
अतः x = 6 व y = 2

UP Board Solutions

प्रश्न 5.
3x – 5y – 4 = 0, 9x = 2y + 7
हलः
समीकरण 3x – 5y – 4 = 0
या 3x – 5y = 4 ….(1)
तथा 9x = 2y + 7
या 9x – 2y = 7 …….(2)
समी० (1) को 3 से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 6

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प्रश्न 6.
29x – 23y = 110 , 23x – 29y = 98
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 7
x का मान समी० (UPBoardSolutions.com) (1) में रखने पर,
29x – 23y = 110
29 × 3 – 23y = 110
87 – 23y = 110
– 23y = 110 – 87
– 23y = 23
y = – 1
अत: x = 3 तथा y = – 1 दी गई समीकरणों के अभीष्ट हल हैं।

UP Board Solutions

प्रश्न 7.
x + y = 5; 2x – 3y = 4 (NCERT)
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 8

UP Board Solutions

Ex 3.2 Pair of Linear Equation (UPBoardSolutions.com) in Two Variables लघु उत्तरीय प्रश्न (Short Answer Type Questions)

निम्नलिखित रैखिक समीकरण युग्म को प्रतिस्थापन या विलोपन विधि से हल कीजिए।
प्रश्न 8.
[latex]\frac{4}{x}[/latex] + 3y = 8; [latex]\frac{6}{x}[/latex] – 4y = – 5
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 9
अतः x = 2 व y = 2

प्रश्न 9.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 10
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 11
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 12

UP Board Solutions

प्रश्न 10.
3x – [latex]\frac{y+7}{11}[/latex] + 2 (UPBoardSolutions.com) = 10 ; 2y + [latex]\frac{x+11}{7}[/latex] = 10
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 13
x = [latex]\frac{1389}{463}[/latex] = 3
x का मान समी० (2) में रखने पर
3 + 14y = 59
14y = 59 – 3
14y = 56
y = [latex]\frac{56}{14}[/latex] = 4
अतः x = 3, y = 4

प्रश्न 11.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 14
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 15
अतः x = 4, y = 5

UP Board Solutions

प्रश्न 12.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 17a
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 17b
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 17
x का मान समी० (6) में रखने पर
3 × 1 – 2y = 1
– 2y = 1 – 3
– 2y = – 2
2y = 2 या y = 1
अतः x = 1 तथा y =1

UP Board Solutions

प्रश्न 13.
99x + 101y = 499; 101x + (UPBoardSolutions.com) 99y = 501
हलः
99x + 101y = 499 …..(1)
101x + 99y = 501 …(2)
समी० (1) में 101 तथा समी० (2) में 99 से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 18
y का मान समी० (1) में रखने पर,
99x + 202 = 499
99x = 499 – 202 = 297
x = [latex]\frac{297}{99}[/latex] = 3
अतः x = 3, y = 2

प्रश्न 14.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 19
(NCERT)
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 20
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 22
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 21

UP Board Solutions

प्रश्न 15.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 23
(NCERT)
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 24
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 25

UP Board Solutions

प्रश्न 16.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 26
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 27
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 28
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 29

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प्रश्न 17.
2(3x – y) (UPBoardSolutions.com) = 5xy; 2(x + 3y) = 5xy
हलः
समीकरण, 2(3x – y) = 5xy
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 30
[latex]\frac{6}{x}[/latex] = 5 – 2 = 3
3x = 6 या x = 2
अतः x = 2, y =1

UP Board Solutions

Ex 3.2 Pair of Linear Equation in Two Variables दीर्घ उत्तरीय प्रश्न (Long Answer Type Questions)

निम्नलिखित रैखिक समीकरण युग्म (UPBoardSolutions.com) को हल कीजिए-

प्रश्न 18.
[latex]\frac{2 x+5 y}{x y}=6 ; \frac{4 x-5 y}{x y}[/latex] = -3 x ≠ 0, y ≠ 0
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 31
अतः x = 1 व y = 2

UP Board Solutions

प्रश्न 19.
[latex]\frac{b x}{a}-\frac{a y}{b}[/latex] + a + b = 0; bx – ay + 2ab = 0
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 32
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 33
अतः x = – a, y = b

UP Board Solutions

प्रश्न 20.
[latex]\frac{b x}{a}-\frac{a y}{b}[/latex] (UPBoardSolutions.com) + a2 + b2 = 0; x + y = 2ab
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 34
x का मान समी० (2) में रखने पर,
ab + y = 2ab
y = 2ab – ab
y = ab
अत: x = ab, y = ab

UP Board Solutions

प्रश्न 21.
2(ax – by) + (a + 4b) = 0; 2(bx + ay) + (b – 4a) = 0
हलः
समीकरण 2(ax – by) + (a + 4b) = 0
या 2ax – 2by = – a – 4b ………(1)
तथा 2(bx + ay) + b – 4a = 0
या 2bx + 2ay = 4a – b
समी० (1) में a तथा समी० (2) में b से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 35

UP Board Solutions

प्रश्न 22.
[latex]\frac{x}{a}+\frac{y}{b}[/latex] = 2; ax – by = a2 – b2
हल:
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 36
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 37
अत: x = 1 व y = 2

प्रश्न 23.
6(ax + by) = 3a + 2b; 6(bx – ay) = 3b – 2a
हलः
समीकरण 6(ax + by) = 3a + 2b
या 6ax + 6by = 3a + 2b …………..(1)
तथा 6(bx – ay) (UPBoardSolutions.com) = 3b – 2a
या 6bx – 6ay = 3b – 2a
समी० (1) में b तथा समी० (2) में a से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 38
6ax = 3a + 2b – 2b
⇒ 6ax = 3a
x = [latex]\frac{3 a}{6 a}[/latex] ⇒ x = [latex]\frac{1}{2}[/latex]
अत: x = [latex]\frac{1}{2}[/latex] व y = [latex]\frac{1}{3}[/latex]

UP Board Solutions

प्रश्न 24.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 39
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 40
y का मान समी० (1) में (UPBoardSolutions.com) रखने पर,
3x + 2 × 13 = 47
या 3x + 26 = 47
3x = 47 – 26 = 21
x = [latex]\frac{21}{3}[/latex] या x = 7
अत: x = 7, y = 13

प्रश्न 25.
152x – 378y = – 74; – 378x + 152y = – 604 (NCERT)
हलः
समीकरण 152x – 378y = – 74 ……….(1)
तथा – 378x + 152y = – 604 ……(2)
समी० (1) में 378 से तथा समी० (2) में 152 से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 41
y का मान समी० (1) में रखने पर,
152x – 378 × 1 = – 74
152x – 378 = – 74
152x = – 74 + 378
152x = 304
या x = [latex]\frac{304}{152}[/latex]
x = 2
अत: x = 2, y = 1

UP Board Solutions

प्रश्न 26.
[latex]\frac{4}{x}[/latex] (UPBoardSolutions.com) + 5y = 7 ; [latex]\frac{3}{x}[/latex] + 4y = 5
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 42
12 + 5y = 7
5y = 7 – 12
5y = – 5
y = [latex]-\frac{5}{5}[/latex] ⇒ y = – 1
अत: x = [latex]\frac{1}{3}[/latex] व y = – 1

प्रश्न 27.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 43
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 44
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 45

UP Board Solutions

प्रश्न 28.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 46
(NCERT)
हलः
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 47
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 48

UP Board Solutions

प्रश्न 29.
ax + by = c; bx + ay = 1 + c
हलः
ax + by = c …………..(1)
bx + ay = 1 + c …………(2)
समी0 (1) में b से तथा समी० (2) में a से गुणा करने पर,
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 49
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.2 50

Balaji Publications Mathematics Class 10 Solutions

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