What is 3xy+2y^2=5,xy-3y^2=-57 ?

The solution to 3xy+2y^2=5,xy-3y^2=-57 is

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3xy+2y^2=5,xy-3y^2=-57

3 x y + 2 y^{2} = 5, x y - 3 y^{2} = - 57

(x = - \frac{9}{4}, x = \frac{9}{4}, y = 4 y = - 4)

Solution steps

[3 x y + 2 y^{2} = 5 x y - 3 y^{2} = - 57]

Isolate

x

for

3 x y + 2 y^{2} = 5 : x = \frac{5 - 2 y ^{2}}{3 y}; y \neq = 0

Plug the solutions

x = \frac{5 - 2 y ^{2}}{3 y}

into

x y - 3 y^{2} = - 57

For

x y - 3 y^{2} = - 57

, subsitute

x

with

\frac{5 - 2 y ^{2}}{3 y} : y = 4, y = - 4

Plug the solutions

y = 4, y = - 4

into

3 x y + 2 y^{2} = 5

For

3 x y + 2 y^{2} = 5

, subsitute

y

with

4 : x = - \frac{9}{4}

For

3 x y + 2 y^{2} = 5

, subsitute

y

with

- 4 : x = \frac{9}{4}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

3 x y + 2 y^{2} = 5, x y - 3 y^{2} = - 57

are

(x = - \frac{9}{4}, x = \frac{9}{4}, y = 4 y = - 4)

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

x + y = 7, x y^{2} x - 3 y + x y = 0

- 2 x^{2} y = 4 - x^{2}, y = 9

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

3 x^{2} - 23 x + 40 = 0, 5 y^{2} - 17 y + 1 y = 0