Question

For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
41x + 53y = 135
53x + 41y = 147

Answer 1

41x + 53y = 135                             ...(1)
53x + 41y = 147                             ...(2)

Adding equation (1) and (2)
        41x + 53y = 135
   +   53x + 41y = 147  
         94x + 94y = 282
Dividing by 94,
            x + y = 3                             ....(3)
Subtracting equation (2) from (1)
        41x + 53y = 135
 -      53x + 41y = 147   
        -      -          -          
        - 12x + 12y = - 12
Dividing by 12,
          - x + y = -1                          ....(4)
Adding (3) and (4)
            x + y = 3
    +   - x + y = -1 
                 2y = 2
                   y = 1

From (3)
x + y = 3
x + 1 = 3
x = 2