$$ \left. \begin{array} { l } { \frac { x - y } { 2 } = \frac { y } { 3 } } \ { x + y = 16 } \ { \Rightarrow x \cdot y = ? } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { \frac { x - y } { 2 } = \frac { y } { 3 } } \ { x + y = 16 } \ { \Rightarrow x \cdot y = ? } \end{array} ight. $$

UpStudy AI · Accepted Answer

Biz quyidagi tenglamalar sistemasini ko'rib chiqamiz:

1) (x – y)/2 = y/3  
2) x + y = 16

Birinchi tenglamani yechish uchun ikki qismning maxrajlarini yo‘q qilish uchun ekvivalent koeffitsient topamiz:

3(x – y) = 2y  
ya'ni, 3x – 3y = 2y  
Shundan 3x = 5y bo‘ladi, demak: x = (5/3)y

Endi bu x ifodasini ikkinchi tenglamada o‘rniga qo‘yamiz:

(5/3)y + y = 16  
(5/3 + 1)y = 16  
(5/3 + 3/3)y = (8/3)y = 16

Shu yerda y ni aniqlash uchun har ikki tomonni 3/8 ga ko‘paytiramiz:
  
y = 16 * (3/8) = 6

Keyinchalik, x ni hisoblaymiz:

x = (5/3) * 6 = 10

Endi x va y ko‘paytmasi:

x ⋅ y = 10 ⋅ 6 = 60

Demak, javob: 60.
x va y ni hisoblash uchun tenglamalar sistemasini yechib, x = 10 va y = 6 topiladi. Shunda x · y = 60.

\( \left. \begin{array} { l } { \frac { x - y } { 2 } = \frac { y } { 3 } } \\ { x + y = 16 } \\ { \Rightarrow x \cdot y = ? } \end{array} \right. \)