Question

If |x-y|=1 and x\y=xy then the number of different pairs of (x,y)which satisfy both the equations simultaneously is

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

4

Step-by-step explanation:

consider two cases x=0, and x not 0. The second equation excludes y=0 automatically so we don’t need it:

i. x/y = xy

If x =0, this is automatically satisfied. Put it in the absolute value:

| 0 - y | = 1

If you know your properties of the absolute value function then you will find that y can be -1 or +1. So now we have two solutions:

(x1,y1) = (0, -1) and (x2,y2) = (0, +1)

Now the second case, when x is not zero:

ii. x/y = xy simplifies to 1 = y^2, as long as x is not zero.

This gives y=-1 and y = +1

For y=-1 the absolute value equation gives:

| x + 1 | = 1.

We have to leave out the choice x=0 (but it was covered before anyway). x=-2 also works. (x3,y3) = (-2, -1). Then we check y=+1:

| x - 1 | =1.

Again we exclude x=0 (but it was also covered before). x=+2 works. (2, 1) works.

To summarize there are four solutions:

(x4, y4) = (2, 1)

(x3, y3) = (-2, -1)

(x2, y2) = (0, 1)

(x1, y1) = (0, -1)