X+ y = 6
2x + y = 4
solve the system of equations by substitution.
(-2, 8)
(2, -8)
no solution
coincident

X+y=6  subtract x from both sides

x=6-y, now use this value of x in the second equation:

2(6-y)+y=4  perform indicated multiplication on left side

12-2y+y=4  combine like terms on left side

12-y=4  subtract 12 from both sides

-y=-8  divide both sides by -1

y=8, now use this y in either original equation to solve for x, I'll use x+y=6

x+8=6  subtract 8 from both sides

x=-2

So the solution to the system of equations is the point (-2, 8)