Question

Solve the following system of equations

Answer 1

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