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)
