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solve for x and y. 2(3x-y)=5xy 2(x+3y)=5xy

Posted by Athreya Bende 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 1 month ago

2(3x - y) = 5xy .(i)
2(x + 3y) = 5xy ..(ii)
Divide eqns. (i) and (ii) by xy,
$\frac { 6 } { y } - \frac { 2 } { x } = 5$ ....(iii)
and $\frac { 2 } { y } + \frac { 6 } { x } = 5$ .....(iv)
Let $\frac { 1 } { y } = a \text { and } \frac { 1 } { x } = b$
then equations (iii) and (iv) become
6a - 2 b = 5 ......(v)
2a -6b = 5 ...(vi)
Multiplying eqn. (v) by 3 and then adding with eqn. (vi),
18a - 6b + 2a - 6b = 15 + 5
20a = 20
$\therefore$ a=1
Substituting this value of a in eqn. (v),
$b = \frac { 1 } { 2 }$
Now $\frac { 1 } { y } = a = 1$
or, y=1
and $\frac { 1 } { x } = b = \frac { 1 } { 2 }$
or, x=2
Hence, x = 2, y = 1

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CBSE > Class 10 > Mathematics