Consider the following pair of equations:

Question

−x − y = −5
y = x + 1

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

(−2, 3)

(3, −2)

(2, 3)

(3, 2)

Answer 1

To find the point at which the two lines intersect, we can solve the system of equations by substituting the value of y from the second equation into the first equation:

−x − (x + 1) = −5
−x - x - 1 = -5
-2x - 1 = -5
-2x = -4
x = 2

Now that we have found x = 2, we can substitute this value back into the second equation to find the value of y:

y = 2 + 1
y = 3

Therefore, the two lines intersect at the point (2, 3). So the correct answer is:

(2, 3)