Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.
So if we substitute x = 4 and y = 1 in the equation, we get:
1 = 3(4)+1
1 = 12+1
1 = 13
The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )
Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.
Substitute x = 0 and y = 1 in the equation as we get:
1 = 3(0)+1
1 = 0 + 1
1 = 1
Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.
Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.
Again, substitute x = 1 and y = 4.
4 = 3(1)+1
4 = 3+1
4 = 4
Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.
Also here's why (4,1) is not the solution of y = 3x + 1
Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.
If we substitute x = 4 in the equation...
y = 3(4)+1
y = 12+1
y = 13
Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.
Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.
(1) For y = 1,
1 = 3x+1
1-1=3x
0=3x
x=0 (Therefore, x = 0 and y = 1)
So the actual order is (0,1).
(2) For y = 13
13 = 3x+1
13-1 = 3x
3x = 12
x = 4 (Therefore, x = 4 and y = 13)
so the actual order for (2) is (4,13).
Basically, (4,1) is false for y = 3x + 1.
