## 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।**

a_{1}x + b_{1}y + 1 = 0

a_{2}x + b_{2}y + c_{1} = 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 = a^{2} – b^{2}

हलः

x + y = a + b

या x + y – (a + b) = 0 …………..(1)

तथा ax – by = a^{2} – b^{2}

या ax – by – (a^{2} – b^{2}) = 0 ……….(2)

अत: x = a, y = b

प्रश्न 3.

a(x + y) + b(x – y) = a^{2} – ab + b^{2}; a(x + y) – b(x – y)= a^{2} + ab + b^{2}

हलः

a(x + y) + b(x – y) = a^{2} – ab + b^{2}

या a(x + y) + b(x – y) – (UPBoardSolutions.com) (a^{2} – ab + b^{2}) = 0 …….(1)

तथा a(x + y) – b(x – y) = a^{2} + ab + b^{2}

या a(x + y) – b(x – y) – (a^{2} + ab + b^{2})= 0 ……..(2)

प्रश्न 4.

ax + by = a^{2}; bx + ay = b^{2}

हलः

समीकरण, ax + by = a^{2}

या ax + by – a^{2} = (UPBoardSolutions.com) 0 ……….(1)

तथा bx + ay = b^{2}

या bx + ay – b^{2} = 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 = m^{2} + n^{2}; x + y = 2m (UPBoardSolutions.com)

हलः

mx – ny = m^{2} + n^{2}

या mx – ny – (m^{2} + n^{2}) = 0 ………(1)

तथा x + y = 2m

या x + y – 2m = 0 …….(2)