What is x+y+xy=-11,x^2+y^2+xy=13 ?

The solution to x+y+xy=-11,x^2+y^2+xy=13 is

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Popular >

x+y+xy=-11,x^2+y^2+xy=13

Solution

x + y + x y = - 11, x^{2} + y^{2} + x y = 13

Solution

x = 4, x = - 3, x = - 1 - 10, x = 10 - 1, y = - 3 y = 4 y = - 1 + 10 y = - 1 - 10

Solution steps

[x + y + x y = - 11 x^{2} + y^{2} + x y = 13]

Isolate

x

for

x + y + x y = - 11 : x = \frac{- 11 - y}{1 + y}; y \neq = - 1

Plug the solutions

x = \frac{- 11 - y}{1 + y}

into

x^{2} + y^{2} + x y = 13

For

x^{2} + y^{2} + x y = 13

, subsitute

x

with

\frac{- 11 - y}{1 + y} : y = - 3, y = 4, y = - 1 + 10, y = - 1 - 10

Plug the solutions

y = - 3, y = 4, y = - 1 + 10, y = - 1 - 10

into

x + y + x y = - 11

For

x + y + x y = - 11

, subsitute

y

with

- 3 : x = 4

For

x + y + x y = - 11

, subsitute

y

with

4 : x = - 3

For

x + y + x y = - 11

, subsitute

y

with

- 1 + 10 : x = - 1 - 10

For

x + y + x y = - 11

, subsitute

y

with

- 1 - 10 : x = 10 - 1

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x + y + x y = - 11, x^{2} + y^{2} + x y = 13

are

x = 4, x = - 3, x = - 1 - 10, x = 10 - 1, y = - 3 y = 4 y = - 1 + 10 y = - 1 - 10

Graph

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Frequently Asked Questions (FAQ)

What is x+y+xy=-11,x^2+y^2+xy=13 ?
The solution to x+y+xy=-11,x^2+y^2+xy=13 is