# RD Sharma Solutions Chapter 3 Pair of Linear Equation in Two Variables Exercise 3.4 Class 10 Maths Chapter Name RD Sharma Chapter 3 Pair of Linear Equation in Two Variables Book Name RD Sharma Mathematics for Class 10 Other Exercises Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.5Exercise 3.6 Related Study NCERT Solutions for Class 10 Maths

### Exercise 3.4 Solutions

Solve each of the following systems of equations by the method of cross - multiplication:

1. x + 2y + 1 = 0
2x - 3y - 12 = 0

Solution 2. 3x + 2y + 25 = 0
2x + y + 10 = 0

Solution

The given system of equation is
3x + 2y + 25 = 0
2x + y + 10 = 0
Here, 3. 2x + y - 35 = 0
3x + 4y - 65 = 0

Solution 4. 2x - y - 6 = 0
x - y - 2 = 0

Solution

The given system of equations may be written as
2x - y - 6 = 0
x - y - 2 = 0
Here, 5. (x+y)/xy = 2
(x-y)/xy = 6

Solution 6. ax + by = a-b
bx - ay = a + b

Solution 7. x + ay - b = 0
ax - by -c = 0

Solution 8. ax + by = a2 .
bx + ay = b2

Solution 9. x/a + y/b = 2
ax - by = a2 - b2

Solution 10. x/a + y/b = a + b

Solution 11. x/a = y/b
ax + by = a2 + b2

Solution 12. 5/(x+y) - 2/(x -y) = -1
15/(x + y) + 7/(x - y) = 10, where x ≠ 0 and  y ≠ 0

Solution 13. 2/x + 3/y = 13
5/x - 4/y = -2 , where x ≠ 0 and y ≠ 0

Solution 14. ax + by = (a + b)/2
3x + 5y = 4

Solution 15. 2ax + 3by = a + 2b
3ax + 2by = 2a + b

Solution 16. 5ax + 6by = 28
3ax + 4by =
18

Solution 17. (a + 2b)x + (2a - b)y = 2
(a - 2b)x + (2a + b)y = 3

Solution 18. x(a- b + ab/a-b) = y(a+ b - ab/a+b)
x + y = 2a2

Solution 19. ax[1/(a-b) - 1/(a+b)] + cy[1/(b-a) - 1/(b+a)] = 2a/(a+b)

Solution 20. (a - b)x + (a+ b)y = 2a2  -  2b2
(a+b)(x+y) = 4ab

Solution 21. a2x + b2y = c2
b2x + a2y = d2

Solution

The given system of equations may be written as
a2x + b2y - c2  = 0
b2x + a2y - d2  = 0
Here, 22. 57/(x+y) + 6/(x-y) = 5
38/(x+y) + 21/(x-y) = 9

Solution 23. 2(ax - by) + a + 4b = 0
2(bx + ay) + b - 4a = 0

Solution

The given system of equation may be written as
2ax - 2by + a +4b = 0
2bx + 2ay + b - 4a = 0
Here, 24. 6(ax + by) = 3a + 2b
6(bx - ay) = 3b - 2a

Solution

The given system of equation is
6(ax + by) = 3a + 2b ...(i)
6(bx - ay) = 3b - 2a ...(ii)
From equation (i), we get
6ax + 6by - (3a + 2b) = 0 ...(iii)
From equation (ii), we get
6bx - 6ay - (3b - 2a) = 0 ...(iv)
Here, Hence, x = 1/2, y = 1/3  is the solution of the given system of equations.

25. a2/x - b2/y = 0
a2b/x + b2a/y = a + b, x, y ≠ 0

Solution

Taking 1/x = u and 1/y = v. Then, the given system of equations become 26. mx - my = m2  + n2
x + y = 2m

Solution

The given system of equations may be written as
mx - ny - (m2  + n2) = 0
x + y - 2m = 0
Here, 27. ax/b - by/a = a+ b
ax - by = 2ab

Solution

The given system of equation may be written as 28.(b/a)x + (a/b)y - (a2  + b2) = 0
x + y - 2ab = 0

Solution 