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# What is the solution set of this system of equations?

y = x^{2} - 3x - 4

x = y + 8

**Solution:**

Given y = x^{2} - 3x - 4 --- (a)

x = y + 8 --- (b)

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

We get x - 8 = x^{2} - 3x - 4

x^{2} - 3x - 4 - x + 8 = 0

x^{2} - 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 = x^{2} - 3x - 4

x = y + 8

**Summary:**

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

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