1. Solve for x and y:         ax + by = a – b;           bx – ay = a + b

2. Find the values of p and q for which the following system of linear
    equations has infinite number of solutions: 2x – y = 5
                                                                         (p + q)x – (2q – p)y = p + 2q + 6
                                                                                 
3. Solve for x and y:         ax + by = 1;                 bx + ay =   2ab
                                                                                                           a² + b²
 
4. Solve for x and y:         217x + 131y = 913 ; 131x + 217y = 827 
 
5. A two digit number is obtained by either multiplying the sum of digits
   by 8 and adding 1, or by multiplying the difference of the digits by 13
  and adding 2. Find the number. How many such numbers are possible?      
 
6. Solve graphically the system of equations:         2x – y = 2;  4x – y = 8.  
    Also find the co-ordinates of points where the line meets the axis of x.
 
7. 8 men and 12 boys can finish a piece of work in 10 days, while 6 men
    and 8 boys can finish it in 14 days. Find the time taken by 2 boys and 3
    men to complete the same work.
 
8. Students of a class are made to stand in rows. If one student is extra in
    a row, there would be two rows less. If one student is less in a row there
    would be three rows more. Find the total number of students in the
    class.
 
9. Use a single graph paper and draw the graphs of following equations:
    2y – x = 8;             5y – x = 14;     y – 2x =1                                           
   Obtain the vertices of triangle so obtained. 

 

 

ANSWERS:
1. x = 1, y = -1,                2. p = q =3               3. x =      a      ,      b                    

                                                                                              a² + b²   a² + b²

4. x = 3, y = 2                5. 41                            6. (3, 4); (1, 0), (2, 0)