−x − y = 1 y = x + 3 if the two equations are graphed, at what point do the lines representing the two equations intersect? (−1, 2) (−2, 1) (1, −2) (2, −1)

The system of linear equations

−x − y = 1
y = x + 3

can be solved in various ways.  This problem hints that you should graph both lines and find the coordinates of their point of intersection.

But we can also solve this system using substitution.  Note that y = x + 3.  We can subst. x + 3 for y in the 1st equation, as follows:

-x - (x+3) = 1.  This simplifies to -x -x - 3 = 1, or -2x = 4, or x = -2.

Since y = x + 3, subbing -2 for x produces y:  y = -2 + 3 = 1

Thus, the solution is (-2, 1). 

−x − y = 1  so y = -x- 1
y = x + 3 
-x - 1 = x + 3
2x = -4
  x = -2

y = -2 + 3 = 1

(-2, 1)

answer
(−2, 1)