Respuesta :

Answer:

Given Two equations :-

[tex]3x {}^{2} - 2 {y}^{2} = 57 .\: .\: .\: . \:(i) \\ - 2 {x}^{2} + 3 {y}^{2} = -23.\: .\: .\: . \:(ii)[/tex]

  • multiplying eq.(i) by 2 eq.(ii) by 3.

[tex](3x {}^{2} - 2 {y}^{2} = 57 ) \times 2 .\: .\: .\: . \:(i) \\ ( - 2 {x}^{2} + 3{y}^{2} = - 23) \times 3.\: .\: .\: . \:(ii)[/tex]

[tex]6x {}^{2} - 4 {y}^{2} =114 .\: .\: .\: . \:(i) \\ - 6 {x}^{2} + 9 {y}^{2} = - 69.\: .\: .\: . \:(ii)[/tex]

[tex]0 + 5 {y}^{2} = 45 \\ 5y {}^{2} = 45 [/tex]

  • diving both sides by 5

[tex] {y}^{2} = 9[/tex]

  • taking Square root

[tex]y = + - 3[/tex]

  • placing this value of y² in eq. (i)

3x²- 2×9 = 57

3x² - 18 = 57

  • adding 18 to both sides

3x² = 57 + 18

3x²= 75

  • diving both sides by 3

x² = 25

x = ± 5

So, the values of x are +5 and -5

and the values of y are +3 and -3

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