a)(x-3) x ( y+4)= -7 b)(x-1) x (xy+1)=2 c)5x + xy - 4y = 9 d)x nhân y = 6 và x + y = 5

Đáp án:

`a)` `( x - 3 ) ( y + 4 ) = -7`

$\bullet$  `{(x - 3 = -1),(y + 4 = 7):}`

`<=>` `{(x = -1 + 3),(y = 7 - 4):}`

`<=>` `{(x = 2),(y = 3):}`

$\bullet$  `{(x - 3 = 7),(y + 4 = -1):}`

`<=>` `{(x = 7 + 3),(y = -1 - 4):}`

`<=>` `{(x = 10),(y = -5):}`

$\bullet$  `{(x - 3 = -7),(y + 4 = 1):}`

`<=>` `{(x = -7 - 3),(y = 1 - 4):}`

`<=>` `{(x = -10),(y = -3):}`

$\bullet$  `{(x - 3 = 1),(y + 4 = -7):}`

`<=>` `{(x = 1 + 3),(y = -7 - 4):}`

`<=>` `{(x = 4),(y = -11):}`

Vậy  `( x ; y ) = ( 2 ; 3 ) ; ( 10 ; 5 ) ; ( -10 ; -3 ) ; ( 4 ; -11 )`.

`b)` `( x - 1 ) ( xy + 1 ) = 2`

$\bullet$  `{(x - 1 = 2),(xy + 1 = 1):}`

`<=>` `{(x = 2 + 1),(xy = 1 - 1):}`

`<=>` `{(x = 3),(3y = 0):}`

`<=>` `{(x = 3),(y = 0):}`

$\bullet$  `{(x - 1 = 1),(xy + 1 = 2):}`

`<=>` `{(x = 1 + 1),(xy = 2 - 1):}`

`<=>` `{(x = 2),(2y = 1):}`

`<=>` $\begin{cases} x = 2\\y = \dfrac{1}{2} \end{cases}$

$\bullet$  `{(x - 1 = -1),(xy + 1 = -2):}`

`<=>` `{(x = -1 + 1),(xy = -2 - 1):}`

`<=>` `{(x = 0),(0 = -3):}` ( loại )

$\bullet$  `{(x - 1 = -2),(xy + 1 = -1):}`

`<=>` `{(x = -2 + 1),(xy = -1 - 1):}`

`<=>` `{(x = -1),(-y = -2):}`

`<=>` `{(x = -1),(y = 2):}`

Vậy  `( x ; y ) = ( 3 ; 0 ) ; ( 2 ; 1/2 ) ; ( -1 ; 2 )`.

`d)` `xy = 6`  và  `x + y = 5`

$\bullet$  `xy = 6`

`<=>` `x = 6/y`

$\bullet$  `x + y = 5`

`<=>` `6/y + y = 5`

`<=>` `6/y + (y^2)/y = (5y)/y`

`<=>` `6 + y^2 = 5y`

`<=>` `5y - y^2 = 6`

`<=>` `y ( 5 - y ) = 6`

$\bullet$  `{(y = -1),(5 - y = -6):}`

`<=>` `{(y = -1),(y = 11):}` ( loại )

$\bullet$  `{(y = -6),(5 - y = -1):}`

`<=>` `{(y = -6),(y = 6):}` ( loại )

$\bullet$  `{(y = -2),(5 - y = -3):}`

`<=>` `{(y = -2),(y = 8):}` ( loại )

$\bullet$  `{(y = -3),(5 - y = -2):}`

`<=>` `{(y = -3),(y = 7):}` ( loại )

$\bullet$  `{(y = 2),(5 - y = 3):}`

`<=>` `{(y = 2),(y = 2):}` ( nhận )

Mà `:` `x + y = 5`

`<=>` `x + 2 = 5`

`<=>` `x = 5 - 2`

`<=>` `x = 3` 

$\bullet$  `{(y = 3),(5 - y = 2):}`

`<=>` `{(y = 3),(y = 3):}` ( nhận )

Mà `:` `x + y = 5`

`<=>` `x + 3 = 5`

`<=>` `x = 5 - 3`

`<=>` `x = 2`

Vậy  `( x ; y ) = ( 2 ; 3 ) ; ( 3 ; 2 )`.