How do you mathematically solve this system: x + y = 6 , 2x + 2y = 12 considering x and y could be either 3 and 3, 5 and 1, or 0 and 6

Question

I'm just a bit confused, because x and y could be at least 3 valid combinations and If I solve the equations I get 0 as result

Answer 1

Your three solutions are correct.

x + y = 6   (multiply this by 2)

we get

2x + 2y = 12

Therefore the two equations are exactly the same straight line graphically.

So this pair of equations have infinite solutions.

(x,y)  =(1,5) , (6,0) , (7,-1) , (4,2) , (-3,9)..........

Hope this helps you understand now.