What is xy^3=-108,(x+y)y=-3 ?

The solution to xy^3=-108,(x+y)y=-3 is

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Popular >

xy^3=-108,(x+y)y=-3

Solution

x y^{3} = - 108, (x + y) y = - 3

Solution

x = - i \frac{3 3}{2}, x = i \frac{3 3}{2}, x = - 4, x = 4, y = 23 i y = - 23 i y = 3 y = - 3

Solution steps

[x y^{3} = - 108 (x + y) y = - 3]

Isolate

x

for

(x + y) y = - 3 : x = - \frac{3}{y} - y; y \neq = 0

Plug the solutions

x = - \frac{3}{y} - y

into

x y^{3} = - 108

For

x y^{3} = - 108

, subsitute

x

with

- \frac{3}{y} - y : y = 23 i, y = - 23 i, y = 3, y = - 3

Plug the solutions

y = 23 i, y = - 23 i, y = 3, y = - 3

into

(x + y) y = - 3

For

(x + y) y = - 3

, subsitute

y

with

23 i : x = - i \frac{3 3}{2}

For

(x + y) y = - 3

, subsitute

y

with

- 23 i : x = i \frac{3 3}{2}

For

(x + y) y = - 3

, subsitute

y

with

3 : x = - 4

For

(x + y) y = - 3

, subsitute

y

with

- 3 : x = 4

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x y^{3} = - 108, (x + y) y = - 3

are

x = - i \frac{3 3}{2}, x = i \frac{3 3}{2}, x = - 4, x = 4, y = 23 i y = - 23 i y = 3 y = - 3

Popular Examples

x+y=425,x+y=309

x + y = 425, x + y = 309

2x+2y=7,x^2-4y^2=8

2 x + 2 y = 7, x^{2} - 4 y^{2} = 8

f(x)=x^2-2x+3,f(x)=-6x

f (x) = x^{2} - 2 x + 3, f (x) = - 6 x

f(x)=5,x+19(x)=x^2+2

f (x) = 5, x + 19 (x) = x^{2} + 2

2y+x=1,x^2-2x+y^2-4y=8

2 y + x = 1, x^{2} - 2 x + y^{2} - 4 y = 8

Frequently Asked Questions (FAQ)

What is xy^3=-108,(x+y)y=-3 ?
The solution to xy^3=-108,(x+y)y=-3 is