Determine the number of solutions for the systems
x+y=2 and 2x+2y=8

The number of solutions of the system is zero

Step-by-step explanation:

we have

a)

Isolate the variable y

----> equation A

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=2

b)

Isolate the variable y

----> equation B

This is the equation of the line in slope intercept form

where

The slope is m=-1

The y-intercept is b=4

Remember that

If two lines are parallel, then their slopes are the same

In this problem the lines A and B are parallel lines with different y-intercept

so

The lines don't intersect

therefore

The system has no solution

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.