Question

Graph the system of equations to determine the solution. In your final answer, include your graph and the solution.

x=y+4
y=x−4

Answer 1

First note both equations are the same line:

x = y + 4 ⇔ x − y = 4 ⇔ y = x − 4

So every point on the line x − y = 4 is a solution (infinitely many solutions).

Some example points on the line: (4,0), (0,−4), (8,4), (2,−2).

Simple ASCII graph (x from −2 to 10, y from −5 to 5). The line is marked with *; axes with | and −; origin labeled O.

y
5| *
4| * (8,4)
3|
2| *
1|
0| * O (4,0)
-1|
-2| *
-3|
-4|* (0,−4)
-5|
----------------------------
-2 0 2 4 6 8 10 x

Solution: All points (x,y) satisfying x − y = 4 (infinitely many).