Consider the following equations:

Question

−x − y = 1
y = x + 3

If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points)

A. (−1, 2)

B. (−2, 1)

C.(1, −2)

D.(2, −1)

Answer 1

To find the point of intersection, we can solve the two equations simultaneously.

From the second equation, we know that y = x + 3. We can substitute this into the first equation:

-x - (x + 3) = 1
-x - x - 3 = 1
-2x - 3 = 1
-2x = 4
x = -2

Now that we have found the x-coordinate of the point of intersection, we can substitute this back into the second equation to find the y-coordinate:

y = -2 + 3
y = 1

Therefore, the point of intersection is (-2, 1), which is option B.