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:
[tex]4(6)+1=-23[/tex][tex]24+1=-23[/tex][tex]25=-23[/tex]As you can see (6,1) is not the solution of this equation, because 25 is not equal to -23.Second equation:
[tex]6+1=7[/tex][tex]7=7[/tex]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.