What is x-y=2,2x^2+9y^2=23 ?

The solution to x-y=2,2x^2+9y^2=23 is

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x-y=2,2x^2+9y^2=23

x - y = 2, 2 x^{2} + 9 y^{2} = 23

(x = 2 + \frac{- 4 + 181}{11}, x = 2 - \frac{4 + 181}{11}, y = \frac{- 4 + 181}{11} y = - \frac{4 + 181}{11})

Solution steps

[x - y = 2 2 x^{2} + 9 y^{2} = 23]

Isolate

x

for

x - y = 2 : x = 2 + y

Plug the solutions

x = 2 + y

into

2 x^{2} + 9 y^{2} = 23

For

2 x^{2} + 9 y^{2} = 23

, subsitute

x

with

2 + y : y = \frac{- 4 + 181}{11}, y = - \frac{4 + 181}{11}

Plug the solutions

y = \frac{- 4 + 181}{11}, y = - \frac{4 + 181}{11}

into

x - y = 2

For

x - y = 2

, subsitute

y

with

\frac{- 4 + 181}{11} : x = 2 + \frac{- 4 + 181}{11}

For

x - y = 2

, subsitute

y

with

- \frac{4 + 181}{11} : x = 2 - \frac{4 + 181}{11}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x - y = 2, 2 x^{2} + 9 y^{2} = 23

are

(x = 2 + \frac{- 4 + 181}{11}, x = 2 - \frac{4 + 181}{11}, y = \frac{- 4 + 181}{11} y = - \frac{4 + 181}{11})

a + b = 4, a^{2} + b^{2} = 2

\frac{1}{2} x + \frac{1}{3} y = 2, \frac{5}{x} - 2 y = \frac{17}{3}

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