Answer to Question #344639 in Algebra for dodo

Question

Solve this system of equations.

(x + 1)² + (y + 1)² = 25,x + y = 5

Answer 1

Solution

From second equation y = 5 – x

Let’s substitute this into first equation:

(x + 1)² + (6 – x)² = 25  =>  2x² – 10x + 37 = 25  =>  x² – 5x + 6 = 0  =>  x₁ = 2, x₂ = 3

Substituting these into second equation y₁ = 3, y₂ = 2

So there are two solutions of the given system of equations:

x₁ = 2, y₁ = 3 and x₂ = 3, y₂ = 2