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x/3 + y/4 =11 5x/6 - …

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x/3 + y/4 =11 5x/6 - y/3=-7

Posted by Umtudokelombi Umtudokelombi 5 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 5 years, 11 months ago

The given equations are
$\frac { x } { 3 } + \frac { y } { 4 } = 11$
$\frac { 5 x } { 6 } - \frac { y } { 3 } = - 7$
Now $\frac { x } { 3 } + \frac { y } { 4 } = 11$
$\Rightarrow$ $\frac { 4 x + 3 y } { 12 } = 11$ (by taking LCM)
$4x + 3y = 132$ ......(i)
$\frac { 5 x } { 6 } - \frac { y } { 3 } = - 7$
$\frac { 5 x - 2 y } { 6 } = - 7$ (by taking LCM)
$5x - 2y = -42$ .........(ii)
Multiplying (i) by 2 and (ii) by 3, we get
$8x + 6y = 264$ ........(iii)
$15x - 6y = -126$ ........(iv)
Adding (iii) from (iv), we get
$23x = 138$ $\Rightarrow$ $x = 6$
Substituting x = 6 in (i),we get
$4 \times 6 + 3 y = 132 \Rightarrow 3 y = 132 - 24$
$3y = 108$
$y = 36$
$\therefore$ Solution is $x = 6, y = 36$

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