First1Last
1 of 1 pages
  1. Answer
    From (i),                      3x = 5 - 4y
    
                                        x = `(5 - 4y)/ 3`.
    
    From (ii),                      2x = 5 - 6y
    
                                         x = `(5 - 6y)/2` .
    
                                       `:. (5 - 4y)/3` = `(5 - 6y)/2` .
    
    Multiply throughout by 6 :
                                    10 - 8y = 15 - 18y.
                                  `:.` 18y - 8y = 15 - 10.
                                  `:.` 10y = 5 and y = `1/2`.
    
    Substitute this value of y in x = `(5 - 6y)/2`.
    
                                            x = `(5 - 3)/2`= `2/2`= 1.
    
    The solution is x = 1; y =`1/2`.

    Explanation: N.B. Here we have found x in terms of y, instead of y in terms of x. Do which is the easier. 


    1. Forum
  2. Answer
    Eliminate y from the questions.
    
    Multiply (1) by 5:    35x + 15y=45
    Multiply (2) by 3:    33x - 15y=57
    
    add:                     68x        =102
    
                            `:.` x = `102/68` =`51/34` =`3/2` =1`1/2`
    
    substitute x = 1`1/2` in the equation 7x + 3y = 9
                                             7(1`1/2`) + 3y = 9
    
                                         `:.` 10`1/2` + 3y = 9 
    
                                                        `:.` 3y = 9 - 10`1/2`
    
                                                                   = - 1`1/2`
                                                     
                                                               `:.` y = -`1/2`
    
    
    Check. when x = 1`1/2` and y = - `1/2`
    
     7x + 3y =7(1`1/2`) + 3(-`1/2`) = 10`1/2` - 1`1/2` = 9.
    
    11x - 5y = 11(1`1/2`) - 5(-`1/2`)=16`1/2`+2`1/2` = 19

    Explanation: Not available 


    1. Forum
  3. Answer
    The perimeter of the rectangle is x 2(x+y) meters.
                                                     
                                                      `:.` 2(x+y) =44.
    
    Divide both sides of this equations by 2;
                                                
                                                  x+y = 22. . . . . . . . . . . . . . . . . . . . .(1) 
    
    
    We are also told that the length is 2 m greater than the width.
    
                                               `:.` x = y+2, 
                                                    x - y = 2 . . . . . . . . . . .  . . . . . . . . .(2)
    
    we have the two equations 
                                 
                                          x + y = 22 . . . . . . . . . . . . .(1)
                                          x - y  = 2  . . . . . . . . . . . . . (2)
    
    add:                                   2x = 24.
                     
                                  `:.`  x = 12.
    
    Substitute in (1) :         12 + y = 22
                    
                                 `:.` y = 10.
    
    The length of the rectangle is 12 m ; its width is 10  m.

    Explanation: Not available 


    1. Forum
  4. Answer
    The cost of 5 oranges and 4 lemons is (5x + 4y) new pence.
    The cost of 3 oranges and 5 lemons is (3x + 5y) new pence.
    
                                              `:.`  5x + 4y =23  . . . . . . . . . . . . . . . . . . .(1) 
                                                      3x + 5y =19  . . . . . . . . . . . . . . . . . . .(2)
    
    Multiply (1) by 3 :        15x + 12y = 69
    Multiply (2)  by 5 :       15x + 25y = 95
    
    Subtract :                     - 13y = - 26  
                                      `:.` y = 2 
    
    substitute in (1)            5x + 8 = 23
    
                                    `:.`5x =23 - 8
    
                                               = 15
    
                                      `:.` x = 3.
    
    The cost of an orange is 3 new pence ; the cost of a lemon is  2 new pence ..

    Explanation: Not available 


    1. Forum
First1Last
1 of 1 pages