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solve for X and Y : 1/(3x+2y) + 3/(3x-2y)=17/5 , 5/(3x+2y)+1/(3x-2y)=2
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Answers
Step-by-step explanation:
Given Equations are:
⇒ (1/3x + 2y) + (3/3x - 2y) = 17/5
⇒ (5/3x + 2y) + (1/3x - 2y) = 2
Let u = 1/3x + 2y, v = 1/3x - 2y.
(i) u + 3v = 17/5
(ii) 5u + v = 2
On solving (i) & (ii) * 3, we get
⇒ u + 3v = 17/5
⇒ 15u + 3v = 6
----------------------
-14u = -13/5
u = 13/70
Substitute u = 13/70 in (i), we get
⇒ u + 3v = 17/5
⇒ (13/70) + 3v = 17/5
⇒ v = 15/14
Hence, (1/3x + 2y) = 13/70 and (1/3x - 2y) = 15/14
⇒ 39x + 26y = 70 ------------- (iii)
⇒ 45x - 30y = 14 --------------- (iv)
On solving (iii) * 15, & (iv) * 13, we get
⇒ 585x - 390y = 182
⇒ 585x + 390y = 1050
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-780y = -868
y = 868/780
y = 217/195.
Substitute y = 217/195 in (iii), we get
⇒ 585x + 390y = 1050
⇒ 585x + 390(217/195) = 1050
⇒ 585x = 616
⇒ x = 616/585.
Therefore,
The values of x and y are: 616/585, 217/195.
Hope it helps!