Question

solve:
57 upon x+y + 6 upon x-y=5
38 upon x+y +21 upon x-y=9


find the value of x and y​

Answer 1

Answer:

x = 11 , y = 8

Step-by-step explanation:

Given :

$\frac{57}{x+y} + \frac{6}{x-y} = 5$

$\frac{38}{x+y} + \frac{21}{x-y} = 9$

Find x & y,.

Solution :

$\frac{57}{x+y} + \frac{6}{x-y} = 5$  ...(i)

$\frac{38}{x+y} + \frac{21}{x-y} = 9$  ...(ii)

By subtracting 2 × (ii) from 7 × (i),

We get,

⇒ $7 \times (i) - 2 \times (i)$

⇒ $7(\frac{57}{x+y} + \frac{6}{x-y}) - 2(\frac{38}{x+y} + \frac{21}{x-y}) = 7 \times 5 - 2 \times 9$

⇒ $\frac{399}{x+y} + \frac{42}{x-y} - (\frac{76}{x+y} + \frac{42}{x-y}) = 35 - 18$

⇒ $\frac{399}{x+y} - \frac{76}{x+y}+ \frac{42}{x-y} - \frac{42}{x-y} = 35 - 18$

⇒ $\frac{399 - 76}{x+y} = 17$

⇒ $\frac{323}{x+y} = 17$

⇒ $323 = 17(x + y)$

⇒ $\frac{323}{17} = x+y$

⇒ $x+y = 19$ ,...(iii)

By subtracting 2 × (i) from 3 × (ii),

We get,.

⇒ $3 \times (ii) - 2 \times (i)$

⇒ $3(\frac{38}{x+y} + \frac{21}{x-y}) - 2(\frac{57}{x+y} + \frac{6}{x-y}) = 9 \times 3 - 5 \times 2$

⇒ $\frac{114}{x+y} + \frac{63}{x-y} - (\frac{114}{x+y} + \frac{12}{x-y}) = 27 - 10$

⇒ $\frac{114}{x+y} - \frac{114}{x+y} + \frac{63}{x-y} - \frac{12}{x-y} = 27 - 10$

⇒ $\frac{63 - 12}{x-y} = 17$

⇒ $\frac{51}{x-y} = 17$

⇒ $51 = 17(x-y)$

⇒ $\frac{51}{17} = x-y$

⇒ $x-y=3$ ...(iv)

By adding (iii) & (iv),

We get,

⇒ $(x + y) + (x - y) =19 + 3$

⇒ $2x=22$

⇒ $x=11$

By subsistuting value of x in (i),

We get,

⇒ $x+y= 19$

⇒ $11 + y = 19$

⇒ $y = 19 - 11$

⇒ $y = 8$