The solution will be posted in a sequential hint based format. You have to verify the steps of hints.

Sequential Hints:

Step 1:

Solution set of sin(\(\frac{x+y}{2}\)) = 0 is {\({x + y = 2n\pi : n \in \mathbb{N}}\)}

– A set of parallel straight lines.

The picture looks like this

Step 2:

Solution set of |x| + |y| = 1 has the picture of a diamond as follows:

Picture of |x|+|y| = 1

Step 3:

Combine the two pictures, please!

See the intersection points!

Step 4:

Find out the intersection line. Find out the solution now. Go to the next problem.