Sum on simultaneous equationSolving this simultaneous equation is little bit hard.The equation 1 y − 2 − 1 x + 2 = 1 60 and 1 x − 1 y = 1 60 .How to solve it please explain.

Question

Sum on simultaneous equationSolving this simultaneous equation is little bit hard.The equation      1          y      −      2        −      1          x      +      2        =      1    60  and      1    x    −      1    y    =      1    60    .How to solve it please explain.

vermieterbx · Accepted Answer

Given equations:                    (1)                                          1                          y              −              2                                      −                              1                          x              +              2                                      =                              1            60                              and                    (2)                                          1            x                          −                              1            y                          =                              1            60                              From (1), we have                                                1                          y              −              2                                      −                              1                          x              +              2                                      =                              1            60                                                      ⟹                                                                (              x              +              2              )              −              (              y              −              2              )                                      (              y              −              2              )              (              x              +              2              )                                      =                              1            60                                              (by cross multiplication)                            ⟹                            60        x        −        60        y        +        240        =        x        y        +        2        y        −        2        x        −        4                            (3)                            ⟹                            x        y        +        62        y        −        62        x        −        244        =        0            Furthermore, from (2) we have                                                1            x                          −                              1            y                          =                              1            60                                                      ⟹                                                  1            x                          =                              1            60                          +                              1            y                          =                                            y              +              60                                      60              y                                                          (4)                            ⟹                            x        =                                            60              y                                      y              +              60                                          Putting the value of x from (4) to (3) yields,                                    (                                                    60                y                                            y                +                60                                              )                ×        y        +        62        y        −        62        ×                  (                                                    60                y                                            y                +                60                                              )                −        244        =        0                                    ⟹                            60                  y                      2                          +        62        y        (        y        +        60        )        −                  (          62          ×          60          )                y        −        244        (        y        +        60        )        =        0                                    ⟹                            122                  y                      2                          −        244        y        −        (        244        ×        60        )        =        0                                    ⟹                                      y                      2                          −        2        y        −        120        =        0                                    ⟹                                      y                      2                          −        12        y        +        10        y        −        (        12        ×        10        )        =        0                                    ⟹                            y        (        y        −        12        )        +        10        (        y        −        12        )        =        0                                    ⟹                                    (        y        +        10        )        (        y        −        12        )        =        0                            (5)                            ⟹                            y        =        −        10        ,        12            Using (4) and (5), the value of x can be found as,                    x        =                                            60              ×              (              −              10              )                                      −              10              +              60                                      ,                                                    60              ×              12                                      12              +              60                                      =        −        12        ,        10

Felix Cohen · Accepted Answer

It&#039;s  x  y  =  62  x  −  62  y  +  244and  x  y  =  60  y  −  60  x  ,which gives  62  x  −  62  y  +  244  =  60  y  −  60  xor  y  =  x  +  2and I hope the rest is smooth.I got   (  10  ,  12  ) and   (  −  12  ,  −  10  )

Sum on simultaneous equation Solving this simultaneous equation is little bit hard. The equation (1)/(y-2) - 1/(x+2)=1/60 and 1/x - 1/y=1/60.

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