Subject: common solution
Who is asking: Student Level: Middle
For the first problem think of (x,y) as a fixed point that is on both graphs, x+y=6 and 2x-3y=2. Since (x,y) is on the first graph the numbers x and y are related by x+y=6. Subtracting x from both sides this relationship becomes y = 6 - x.
Since (x,y) is also on the graph of the second equation the numbers x and y satisify the second equation 2x-3y=2. But we know that y = 6 - x and hence
For the second problem you are looking for an expression that is equivalent to 3x - y = 4 which is of the form
-y = 4 - 3x