The number of ordered pairs (x, 1) satisfying the equations x+ y= (x+y) and |x|+|y|=1 is

Step-by-step solution

x+ y= (x+y)2 (x+y) 2 (x-y) 2 =2 (x+y) 2 (x+y) 2 (x+y) 2 [ (x-y) 2 - (x+y) 2 ]=0 (x+y) 2 x 2 y 2 =0 Either x+y 2 =0 or x 2 =0 or y 2 =0 x+y=0 or x=0 or y=0 Also |x|+|y|=1 x+y=1, x-y=1x+y=-1, x-y=-1 Thus solving x+y=0 with x-y=1 or x-y=-1 We get ( 1 2 , -1 2 ) or (- 1 2 , 1 2 ) Solving with x=0 , we get (0, 1) Solving with y=0 we get ( 1,0) So, we get 6 orderd pairs.