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Arisa [49]
3 years ago
6

Solve the following system of equations

Mathematics
1 answer:
erastova [34]3 years ago
6 0

Answer:

Given Two equations :-

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

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

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

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

0 + 5 {y}^{2}  = 45 \\ 5y {}^{2}  = 45

  • diving both sides by 5

{y}^{2}  = 9

  • taking Square root

y =  +  - 3

  • <u>placing this value of y² in eq. (i)</u>

3x²- 2×9 = 57

3x² - 18 = 57

  • adding 18 to both sides

3x² = 57 + 18

3x²= 75

  • diving both sides by 3

x² = 25

<u>x = ± 5</u>

<h3>So, the values of x are <u>+5 and -5</u> </h3><h3>and the values of y are <u>+3 and -3</u></h3>
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