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

Exercise 3.4

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

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

Solution

The given system of equation is Hence, the solution of the given system of equations is  x = 3, y = -2.

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

Solution

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

Solution

The given system of equations may be written as Hence,  x = 15, y = 5 is the solution of the given system of equations.

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

Solution

The given system of equations may be written as 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 Hence, x = 1, y = 1 is the solution of the given system of the equations.

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

Solution

The given system of equations may be written as 8. ax + by = a2
bx + ay = b2

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 ≠ 0 and y ≠ 0

Solution 10. 2/x + 3/y = 13
5/x - 4/y = -2
where x ≠ 0 and y ≠ 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 = 8
Hence we get the value of x = 11 and y = 8 .

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

Solution

The system of the given equations may be written as . 13. x/a + y/b = a+b
x/a2 + y/b2 = 2

Solution Hence we get the value = a2 and y = b2

14. x/a = y/b
ax + by = a2 + b2

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

Solution

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 = 2a2

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 = 2a2 - 2a2
(a+b) (x+y) = 4ab

Solution

The given system of equation is 21. a2x + a2y = c2
b2x + a2y = d2

Solution

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

Solution 25. a2/x - b2/y = 0
a2b/x + c2a/y = a + b, x,y ≠ 0

Solution 26. mx - my = m2 + n2
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 - (a2 + b2) = 0
x + y - 2ab = 0

Solution

The given system of equation may be written as 