Question

Solve the following system of equations

Answer 1

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

$y = + - 3$

• 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