

To know if the solution is (6 , 1) you use the value of x and y in the solution(x,y) in both equations and prove if the result is a real math expressioon.
In the first equation:



As you can see (6,1) is not the solution of this equation, because 25 is not equal to -23.
Second equation:


As the given coordinates for the solution (6,1) applies only as a solution of the second equation. This is not the solution of the system of linear equations.