What is x^2+y^2=26,x+y=4 ?

The solution to x^2+y^2=26,x+y=4 is

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x^2+y^2=26,x+y=4

x^{2} + y^{2} = 26, x + y = 4

(x = - 1, x = 5, y = 5 y = - 1)

Solution steps

[x^{2} + y^{2} = 26 x + y = 4]

Isolate

x

for

x + y = 4 : x = 4 - y

Plug the solutions

x = 4 - y

into

x^{2} + y^{2} = 26

For

x^{2} + y^{2} = 26

, subsitute

x

with

4 - y : y = 5, y = - 1

Plug the solutions

y = 5, y = - 1

into

x + y = 4

For

x + y = 4

, subsitute

y

with

5 : x = - 1

For

x + y = 4

, subsitute

y

with

- 1 : x = 5

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x^{2} + y^{2} = 26, x + y = 4

are

(x = - 1, x = 5, y = 5 y = - 1)

- x + 2 y = 4, x - 2 y = 4

\frac{4}{x} + \frac{3}{y} = 2, 4 x + 3 y = 25

x y = 1, 2 (x - 1) (y + 2) = 15

y = x^{2} - 2 x + 3, y = - 5 x + 1

2 x + 5 \frac{y}{x} y = 6, 4 x - 5 \frac{y}{x} y = - 3