Free PDF download of UP Board Solutions for Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.3, are provided here, contain detailed explanations of all the problems mentioned in the UP Board Solutions. Students should solve questions from these UP Board solution of class 10, which will help them to prepare well for their exams.
Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.3 दो चर वाले रैखिक समीकरण युग्म
निम्नलिखित रैखिक समीकरण निकाय को (UPBoardSolutions.com) ब्रज – गुणन विधि द्वारा हल कीजिए।
a1x + b1y + 1 = 0
a2x + b2y + c1 = 0
प्रश्न 1.
2x + y – 35 = 0; 3x + 4y – 65 = 0
हलः
समीकरण 2x + y – 35 = 0 ……..(1)
3x + 4y – 65 = 0 …(2)
प्रश्न 2.
x + y = a + b; ax (UPBoardSolutions.com) – by = a2 – b2
हलः
x + y = a + b
या x + y – (a + b) = 0 …………..(1)
तथा ax – by = a2 – b2
या ax – by – (a2 – b2) = 0 ……….(2)
अत: x = a, y = b
प्रश्न 3.
a(x + y) + b(x – y) = a2 – ab + b2; a(x + y) – b(x – y)= a2 + ab + b2
हलः
a(x + y) + b(x – y) = a2 – ab + b2
या a(x + y) + b(x – y) – (UPBoardSolutions.com) (a2 – ab + b2) = 0 …….(1)
तथा a(x + y) – b(x – y) = a2 + ab + b2
या a(x + y) – b(x – y) – (a2 + ab + b2)= 0 ……..(2)
प्रश्न 4.
ax + by = a2; bx + ay = b2
हलः
समीकरण, ax + by = a2
या ax + by – a2 = (UPBoardSolutions.com) 0 ……….(1)
तथा bx + ay = b2
या bx + ay – b2 = 0 ……(2)
प्रश्न 5.
हलः
प्रश्न 6.
2ax + 3 by = a + 2b; 3ax + 2by = 2a + b
हलः
2ax + 3by = a + 2b (UPBoardSolutions.com)
या 2ax + 3by – (a + 2b) = 0 ………..(1)
तथा 3ax + 2by = 2a + b
या 3ax + 2by – (2a + b) = 0 ………..(2)
प्रश्न 7.
हलः
प्रश्न 8.
6(ax + by) = 3a + 2b; 6(bx – ay) = 3b – 2a
हलः
समीकरण 6(ax + by) (UPBoardSolutions.com) = 3a + 2b
या 6ax + 6by – (3a + 2b) = 0 ………(1)
तथा 6 (bx – ay) = 3b – 2a
या 6bx – 6ay – (3b – 2a) = 0 ………….(2)
प्रश्न 9.
=(UPBoardSolutions.com) a + b; ax – by = 2ab
हलः
प्रश्न 10.
हलः
प्रश्न 11.
mx – ny = m2 + n2; x + y = 2m (UPBoardSolutions.com)
हलः
mx – ny = m2 + n2
या mx – ny – (m2 + n2) = 0 ………(1)
तथा x + y = 2m
या x + y – 2m = 0 …….(2)