## Chapter 3 Pair of Linear Equations in Two Variables R.D. Sharma Solutions for Class 10th Math Exercise 3.4

**Exercise 3.4**

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

1. x + 2y + 1 = 0

2x - 3y - 12 = 0

The given system of equation is

Hence, the solution of the given system of equations isÂ x = 3, y = -2.

2. 3x + 2y + 25 = 0

2x + y + 10 = 0

The given system of equation is

Hence, x = 5, y = -20 is the solution of the given system of equations.

3. 2x + y - 35 = 0

3x + 4y - 65 = 0

The given system of equations may be written asÂ

Hence,Â x = 15, y = 5 is the solution of the given system of equations.

4. 2x - y - 6 = 0

x - y - 2 = 0Â

The given system of equations may be written as

5. (x+y)/xy = 2

(x-y)/xy = 6

The given system of equations is

6. ax + by = a - b

bx - ay = a + b

The given system of equations is

Hence, x = 1, y = 1 is the solution of the given system of the equations.

7. x + ay - b = 0

ax - by - c = 0

The given system of equations may be written as

8. ax + by = a

bx + ay = b

The system of the given equations may be written as

The given system of equation is

11. 57/(x+y) + 6/(x-y) = 5

38/(x+y) + 21/(x-y) = 9

Hence we get the value of x = 11 and y = 8 .

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

3ax + 2by = 2a + b

Â The given system of equations is

16. 5ax + 6by = 28

3ax + 4by - 18 = 0

The given system of equation is

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

(a-2b)x + (2a+b)y = 3

The given system of equations may be written as

The given system of equation is

19. bx + cy = a + b

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

The given system of equation is

20. (a-b)x + (a+b)y =Â 2a

The given system of equation is

21.Â a

The given system of equations may be written as

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

2(bx+ay) + b - 4a = 0

The given system of equation may be written as

26. mx - my = m

x + y = 2m

The given system of equations may be written as

The given system of equation may be written as

28. bx/a + ay/b - (a

x + y - 2ab = 0

The given system of equation may be written as

1. x + 2y + 1 = 0

2x - 3y - 12 = 0

**Solution**The given system of equation is

2. 3x + 2y + 25 = 0

2x + y + 10 = 0

**Solution**The given system of equation is

3. 2x + y - 35 = 0

3x + 4y - 65 = 0

**Solution**The given system of equations may be written asÂ

4. 2x - y - 6 = 0

x - y - 2 = 0Â

**Solution**The given system of equations may be written as

Â

Hence , x = 4, y = 2 is the solution of the given system of the equations.5. (x+y)/xy = 2

(x-y)/xy = 6

**Solution**The given system of equations is

6. ax + by = a - b

bx - ay = a + b

**Solution**The given system of equations is

7. x + ay - b = 0

ax - by - c = 0

**Solution**The given system of equations may be written as

^{2}bx + ay = b

^{2}**Solution**The system of the given equations may be written as

9. 5/(x+y) - 2/(x-y) = -1

15/(x+y) + 7/(x-y) = 10

where x â‰ 0 and yÂ â‰ 0

**Solution**

10. 2/x + 3/y = 13

5/x - 4/y = -2

where x â‰ 0 and yÂ â‰ 0

**Solution**The given system of equation is

11. 57/(x+y) + 6/(x-y) = 5

38/(x+y) + 21/(x-y) = 9

**Solution**

Now adding eq.(3) and (4) we get x = 11

And after substituting the value of x in eq. (4) we get y = 8Hence we get the value of x = 11 and y = 8 .

12. x/a + y/b = 2

ax-by = a

^{2}- b^{2}**Solution**

The system of the given equations may be written as .

13. x/a + y/b = a+b

x/a

^{2}Â + y/b^{2}Â = 2**Solution**

Hence we get the value = a

^{2}Â and y = b^{2}
14. x/a = y/b

ax + by =Â a

^{2}Â +Â b^{2}Â**Solution**15. 2ax + 3by = a + 2b

3ax + 2by = 2a + b

**Solution**Â The given system of equations is

16. 5ax + 6by = 28

3ax + 4by - 18 = 0

**Solution**The given system of equation is

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

(a-2b)x + (2a+b)y = 3

**Solution**The given system of equations may be written as

18. x[a-b + ab/(a-b)] = y[a+b - ab/(a+b)]

x+y = 2a

^{2}**Solution**The given system of equation is

19. bx + cy = a + b

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

**Solution**The given system of equation is

20. (a-b)x + (a+b)y =Â 2a

^{2}- 2a^{2}
(a+b) (x+y) = 4ab

**Solution**The given system of equation is

21.Â a

^{2}x +Â a^{2}y =Â c^{2}
b

^{2}x +Â a^{2}y =Â d^{2}**SolutionÂ**The given system of equations may be written as

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

Â

24. 6(ax + by) = 3a + 2b

6(bx - ay) = 3b - 2a

**Solution**
25. a

^{2}/x -Â b^{2}/y = 0
a

^{2}b/x +Â c^{2}a/y = a + b, x,y â‰ 0

**Solution**26. mx - my = m

^{2}Â + n^{2}x + y = 2m

**Solution**The given system of equations may be written as

27. ax/b - by/a = a+b

ax - by = 2ab

**Solution**The given system of equation may be written as

28. bx/a + ay/b - (a

^{2}Â + b^{2}) = 0x + y - 2ab = 0

**Solution**The given system of equation may be written as