What I showed you was a proof that the point given does not lie on either of the lines. If the point is not on the line, then it cannot be the solution.

A point that lies on the line would give you the y value back when you plugged in x. For example, if you wanted to know if (1,6) is a solution to y = 2x +4. We plug in x = 1

y = 2*1 + 4

y = 2 + 4

y = 6

Since 6 is also the value given by the point, it is a solution for the line.

Another way you could have solved the original problem, would be to solve the system of equations like any other and ignore the point. If the solution you reach is the same as the point then you know that the point is the solution to the system of equations.

y=2x+1 y=-2/3x-3

Solve the system:

2x + 1 = -2/3x - 3

8/3x = - 4

x = -4*3/8

x = - 3/2

y = 2*-3/2 + 1

y = -3 + 1

y = -2

Solution to the system of equations is (-3/2 , -2) and not the point (3 , -4)