CPhill, if you can help me one last time!!

Thanks, Enquired.....glad to help.....!!!

4x+5y=23

4x-y=5

Notice that the second equation  can be rearranged as :

4x  = 5 + y

And substituting this into the first equation for 4x, we have

5 + y + 5y  = 23

5 + 6y  = 23      subtract 5 from both sides

6y  = 18           divide both sides by 6

y = 3

So

4x = 5 + y

4x = 5 + 3    

4x = 8     divide both sides by 4

x = 2

So   (x , y)  = ( 2, 3)