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)
