Maths 1 Practice Set 1.2

     
 Practice Set 1.2 
  Q 1 Complete the following table tu draw
    graph of the equation -
        1] x + y = 3 
                

                     

                      
 x 
                      
 3 
                      
 2 
                      
 0 
                    
                    

                      
 y 
                      
 0 
                      
 5 
                      
 3 
                    
                    

                      
 (x,y) 
                      
 (3,0) 
                      
 (-2,5) 
                      
 (0,3) 
                    
  
                
             2] x - y = 4
                     

                         

                          
 x 
                          
 4 
                          
 -1 
                          
 0 
                        
                        

                          
 y 
                          
 0 
 
                          
 -5 
                          
 -4 
                        
                        

                          
 (x,y) 
                          
 (4,0) 
                          
 (-1,-5) 
                          
 (0,-4) 
                        
  
                    
  1]Q 2 Solve the following equations graphically.
 1] x + y = 6 ; x - y = 4
     x + y = 6              
     .`. y = 6 - x
      

         

            
 x 
            
 0 
            
 6 
            
 3 
            
 4 
         
         
 
            
 y 
            
 6 
            
 0 
            
 3 
            
 2 
         
         

            
(x,y)
            
(0,6)
            
(6,0)
            
(3,3)
            
(4,3)
         
         
      x - y = 4
      .`. y = x - 4
       

          

            
 x 
            
 0 
            
 4 
            
 2 
            
 5 
         
         
 
            
 y 
            
 -4 
            
 0 
            
 -2 
            
 1 
         
         

            
(x,y)
            
(0,-4)
            
(4,0)
            
(2,-2)
            
(5,1)
         
         
         

         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
         
 
 The two lines intersect at point (5,1).
  .`. x = 5 and y = 1 is the
  solution 
      of the equation 
      x + y = 6 and x - y = 4 .

  
  
2] x + y = 5 ; x - y = 3
    x + y = 5
    .`. y = 5 - x
       

          

            
 x 
            
 0 
            
 5 
            
 2 
            
 3 
         
         
 
            
 y 
            
 5 
            
 0 
            
 3 
            
 2 
         
         

            
(x,y)
            
(0,5)
            
(5,0)
            
(2,3)
            
(3,2)
         
         
    x - y = 3
    .`. y = x - 3
       

          

            
 x 
            
 0 
            
 3 
            
 2 
            
 1 
         
         
 
            
 y 
            
 -3 
            
 0 
            
 -1 
            
 -2 
         
         

            
(x,y)
            
(0,-3)
            
(3,0)
            
(2,-1)
            
(1,-2)
         
         
 
    

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
  The two lines intersect at point (4,1).
  .`. x = 4 and y = 1 is the solution of 
  simultaneous equation
  x + y = 5 and x - y = 3 .
  
3] x + y = 0 ; 2x - y = 9
    x + y = 0
    .`. y = -x
       

          

            
 x 
            
 0 
            
 2 
            
 -2 
            
 -1 
         
         
 
            
 y 
            
 0 
            
 -2 
            
 2 
            
 1 
         
         

            
(x,y)
            
(0,0)
            
(2,-2)
            
(-2,2)
            
(-1,1)
         
         
         
    2x - y = 9
    .`. y = 2x - 9
         

          

            
 x 
            
 0 
            
 2 
            
 5 
            
 4 
         
         
 
            
 y 
            
 -9 
            
 -5 
            
 1 
            
 -1 
         
         

            
(x,y)
            
(0,-9)
            
(2,-5)
            
(5,1)
            
(4,-1)
         
         
    

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    The two lines intersect at point (3,-3)
    .`. x = 3 and y = -3 is the solution of
    the simultaneous equation
    x + y = 0 and 2x - y = 9 .
    
    
4] 3x - y = 2 ; 2x - y = 3
    3x - y = 2
    .`. y = 3x - 2
       

          

            
 x 
            
 0 
            
 1 
            
 -1 
            
 2 
         
         
 
            
 y 
            
 -2 
            
 1 
            
 -5 
            
 4 
         
         

            
(x,y)
            
(0,-2)
            
(1,1)
            
(-1,-5)
            
(2,4)
         
         
    2x - y = 3         
    .`. y = 2x - 3
        

          

            
 x 
            
 0 
            
 1 
            
 2 
            
 3 
         
         
 
            
 y 
            
 -3 
            
 -1 
            
 1 
            
 3 
         
         

            
(x,y)
            
(0,-3)
            
(1,-1)
            
(2,1)
            
(3,3)
         
         
      

       
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    The two lines intersect at point (-1,-5)
    .`. x = -1 and y = -5 is the solution of
    the simultaneous equation
    3x - y = 2 and 2x - y = 3 .
    
    
5] 3x - 4y = -7 ; 5x -2y = 7
    3x - 4y = -7
    .`. 4y = 3x + 7
    .`. y = 3x + 7
               4
        

          

            
 x 
            
 -1 
            
 -5 
            
 3 
            
 5 
         
         
 
            
 y 
            
 1 
            
 -2 
            
 4 
            
 5.5 
         
         

            
(x,y)
            
(-1,1)
            
(-5,-2)
            
(3,4)
            
(5,5.5)
         
         
    5x - 2y = 0
    .`. 2y = 5x
    .`. y =  5  x
             2
       

          

            
 x 
            
 0 
            
 2 
            
 -2 
            
 1 
         
         
 
            
 y 
            
 0 
            
 5 
            
 -5 
            
 2.5 
         
         

            
(x,y)
            
(0,0)
            
(2,5)
            
(-2,-5)
            
(1,2.5)
         
         
 
      
  
         
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    The two lines intersect at point (1,2.5)
    .`. x = 1 and y = 2.5 is the solution of
    the simultaneous equation
    3x - 4y = -7 and 5x -2y = 7 .
    
6] 2x - 3y = 4 ; 3y - x = 4
    2x - 3y = 4
    .`. 3y = 2x - 4
    .`. y = 2x - 4
               3 
       

          

            
 x 
            
 2 
            
 -1 
            
 5 
            
 8 
         
         
 
            
 y 
            
 0 
            
 -2 
            
 2 
            
 4 
         
         

            
(x,y)
            
(2,0)
            
(-1,-2)
            
(5,2)
            
(8,4)
         
         
    3y - x = 4
    .`. 3y = x + 4
    .`. y =  x + 4
               3
       

          

            
 x 
            
 2 
            
 -4 
            
 5 
            
 -1 
         
         
 
            
 y 
            
 2 
            
 0 
            
 3 
            
 1 
         
         

            
(x,y)
            
(2,2)
            
(-4,0)
            
(5,3)
            
(-1,1)
         
         
        
 
         
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
       
    The two lines intersect at point (8.4)
    .`. x = 8 and y = 4 is the solution of
    the simultaneous equation
     2x - 3y = 4 and 3y - x = 4 .