What is x-y=1,x^3-y^3=7 ?

The solution to x-y=1,x^3-y^3=7 is

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x-y=1,x^3-y^3=7

x - y = 1, x^{3} - y^{3} = 7

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

Solution steps

[x - y = 1 x^{3} - y^{3} = 7]

Isolate

x

for

x - y = 1 : x = 1 + y

Plug the solutions

x = 1 + y

into

x^{3} - y^{3} = 7

For

x^{3} - y^{3} = 7

, subsitute

x

with

1 + y : y = 1, y = - 2

Plug the solutions

y = 1, y = - 2

into

x - y = 1

For

x - y = 1

, subsitute

y

with

1 : x = 2

For

x - y = 1

, subsitute

y

with

- 2 : x = - 1

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x - y = 1, x^{3} - y^{3} = 7

are

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

x^{2} + y^{2} + 6 x + 2 y = 0, x + y + 8 = 0

x + 157 x + 15 y = 2 x^{2} x, y = 7

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

x y = - 4, 3 x + 4 y = - 22

x^{2} + y^{2} + 6 x + 2 y = 0, x + y = - 8