Balaji Class 10 Maths Solutions Chapter 3 Pair of Linear Equation in Two Variables Ex 3.3

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.
[latex]\frac{a x}{b}-\frac{b y}{a}[/latex] =(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)

Balaji Publications Mathematics Class 10 Solutions