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Solve for x and y : 2(3x-y)=5xy, 2(x+3y)=5xy

Posted by Richa Kumari 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

2(3x - y) = 5xy .(i)

2(x + 3y) = 5xy ..(ii)

Divide eqns. (i) and (ii) by xy,

{tex}\frac { 6 } { y } - \frac { 2 } { x } = 5{/tex} ....(iii)

and {tex}\frac { 2 } { y } + \frac { 6 } { x } = 5{/tex} .....(iv)

Let {tex}\frac { 1 } { y } = a \text { and } \frac { 1 } { x } = b{/tex}

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

{tex}\therefore {/tex} a=1

Substituting this value of a in eqn. (v),

{tex}b = \frac { 1 } { 2 }{/tex}

Now {tex}\frac { 1 } { y } = a = 1{/tex}

or, y=1

and {tex}\frac { 1 } { x } = b = \frac { 1 } { 2 }{/tex}

or, x=2

Hence, x = 2, y = 1

0Thank You

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