RD Sharma Solutions Chapter 3 Pair of Linear Equation in Two Variables Exercise 3.4 Class 10 Maths

RD Sharma Solutions for Class 10 Chapter 3 Pair of Linear Equation in Two Variables Exercise 3.4

Chapter Name

RD Sharma Chapter 3 Pair of Linear Equation in Two Variables

Book Name

RD Sharma Mathematics for Class 10

Other Exercises

  • Exercise 3.1
  • Exercise 3.2
  • Exercise 3.3
  • Exercise 3.5
  • Exercise 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

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