# What is the solution to the following system of equations?

y = x^{2} + 10x + 11, y = x^{2} + x - 7

**Solution: **

Given set of equations y = x^{2} + 10x + 11 --- (1)

y = x^{2} + x - 7 --- (2)

Solving the equations by elimination method

⇒ Subtracting equation 2 from eq 1 we get,

⇒ y - y = x^{2} + 10x + 11 - (x^{2} + x - 7)

⇒ 0 = x^{2} + 10x + 11 - x^{2} - x + 7

⇒ 0 = 9x + 18

⇒ 9x = -18

⇒ x = -2

Put the value of x in eq 1 we get

⇒ y = (-2)^{2} + 10(-2) + 11

⇒ y = 4 - 20 + 11

⇒ y = -5

## What is the solution to the following system of equations?

y = x^{2 }+ 10x + 11, y = x² + x - 7

**Summary: **

The solution to the following set of equations y = x^{2} + 10x + 11, y = x^{2} + x - 7 is (-2, -5).