# The number of of integral ordered pairs (x,y) satisfying the system of given equations

Question

The number of integral ordered pairs ($$x,y$$) satisfying the system of given equations $$|x+y-4| = 5$$ .........(i)and

$$|x-3|+|y-1| = 5$$ .....(ii) is/are

(A)2

(B)4

(C)6

(D)12

My attempt I first used $$x+y-4=5$$ as one equation and $$x+y-=-5$$ as other and similarly obtained four equations from equation (ii) but could not get to the answer please tell me if the method is wrong itself or maybe the last step miscalculations are the reasons of not getting the answer

Rewrite the first equation $|x+y-4| = 5$ as

$x = - y - 1$

or

$x = 9 - y$

and rewrite the second equation $|x-3|+|y-1| = 5$ as

$x = |y-1| - 2,\:\:\:\:$ $|y-1|<5$

or

$x = 8 - |y-1|,\:\:\:\:$ $|y-1|<5$

or

$x = 3\:$ and $\:|y-1|=5$

and work out the solution from there.

• so that means the method I used was right @JKnecht – Nitro phenol May 6 '16 at 5:05