100 points, will mark brainliest Explain why (4, 1) is not a solution to the equation y = 3x + 1.

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.

See below

Step-by-step explanation:

Given the point (4,1) means

(x,y) = (4,1)

So, x = 4 , y = 1

Given the equation y = 3x+1

Put x = 4 and y = 1

=> 1 = 3(4)+1

=> 1 = 12 + 1

=> 1 ≠ 13

Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1