What is 4xy-2x^2=-6,6x+3y=-6 ?

The solution to 4xy-2x^2=-6,6x+3y=-6 is

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4xy-2x^2=-6,6x+3y=-6

4 x y - 2 x^{2} = - 6, 6 x + 3 y = - 6

(x = \frac{19 - 2}{5}, x = - \frac{2 + 19}{5}, y = - \frac{6 + 2 19}{5} y = \frac{2 19 - 6}{5})

Solution steps

[4 x y - 2 x^{2} = - 6 6 x + 3 y = - 6]

Isolate

x

for

6 x + 3 y = - 6 : x = - \frac{y + 2}{2}

Plug the solutions

x = - \frac{y + 2}{2}

into

4 x y - 2 x^{2} = - 6

For

4 x y - 2 x^{2} = - 6

, subsitute

x

with

- \frac{y + 2}{2} : y = - \frac{6 + 2 19}{5}, y = \frac{2 19 - 6}{5}

Plug the solutions

y = - \frac{6 + 2 19}{5}, y = \frac{2 19 - 6}{5}

into

6 x + 3 y = - 6

For

6 x + 3 y = - 6

, subsitute

y

with

- \frac{6 + 2 19}{5} : x = \frac{19 - 2}{5}

For

6 x + 3 y = - 6

, subsitute

y

with

\frac{2 19 - 6}{5} : x = - \frac{2 + 19}{5}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

4 x y - 2 x^{2} = - 6, 6 x + 3 y = - 6

are

(x = \frac{19 - 2}{5}, x = - \frac{2 + 19}{5}, y = - \frac{6 + 2 19}{5} y = \frac{2 19 - 6}{5})

f (x) = x^{2} - 5 x + 3, f (x) = - 3

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

2 x - 5 y = - 3, 2 x - 5 y = 3

x - y = 9, x \cdot y = 14

3 y + 43 = - 2, 5 x^{8} y - 12 x = 32