To solve this equation, I would use substitution. The first equation is #x+y=10#. The second equation is #y=x-6#. Substitute the second equation into the first one and simplify.

#color(red)(x+y=10)# and #color(blue)(y=x-6)#

#color(red)x+(color(blue)(x-6))=color(red)10#

#color(purple)(2x-6=10)#

#color(purple)(2x-6)+6=color(purple)10+6#

#color(purple)(2x=16)#

#color(purple)(2x)/2=color(purple)16/2#

#color(purple)(x=8)#

Once you have solved for #x#, DO NOT FORGET to solve for #y#. Plug #color(purple)(x=8)# in for #x# in either of the original equations and simplify for #y#. I am going to solve for #y# using the second equation.

#color(blue)(y=x-6)#

#color(blue)(y=)color(purple)8color(blue)(-6)#

#color(blue)(y=2)#

Write your final answer as a coordinate point: **(8,2)**