y=x-6
subsitute x-6 for y in other equation
y=8x+1
x-6=8x+1
minus x from both sides
-6=7x+1
minus 1 both sides
-7=7x
divide by 7 both sides
-1=x
x=-1
subsitue back
y=-1-6
y=-7
x=-1 and y=-7 or in (x,y) form, (-1,-7)
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