The system of equation |x−1|+3y=4,x−|y−1|=2  has

The given equation is |x−1|+3y=4        ⇒  {x+3y=5,     x≥1                        .......(i)−x+3y=3,   x<1                       .........(ii) and    x−|y−1|=2 ⇒  {x−y=1,      y≥1                      ..........(iii)x+y=3,      y<1                      ...........(iv)  Solving Eqs. (i) and (iii), we get                x=2,  y=1 Solving Eqs. (i) and (iv), we get    x=2,      y=1  no solution       (∵    x≥1,   y<1) Solving Eqs. (ii) and (iv), we get  x=52,     y=32  no solution           (∵      x<1,  y<1) Hence, solution is x=2,y=1   (a unique solution).