What is the solution set of this system of equations?
y = x² - 3x - 4
x = y + 8 

Solution:

Given y = x² - 3x - 4 --- (a)

x = y + 8 --- (b)

By solving the linear equations (a) and (b) by substitution method

We get x - 8 = x² - 3x - 4

x² - 3x - 4 - x + 8 = 0

x² - 4x + 4 = 0

(x - 2)² = 0

x = 2

Put x = 2 in eq(b),

We get, 2 = y + 8

y = 2 - 8

y = -6

What is the solution set of this system of equations?
y = x² - 3x - 4
x = y + 8

Summary:

The solution set of this system of equations y = x² - 3x - 4 and x = y + 8 are (2, -6).