Question

Please answer this question:-

$\frac{y + 6}{x} = \frac{y - 6}{3x}$

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Answer 1

GIVEN:-

$\large{\sf{\dfrac{y + 6}{x} =\dfrac{y - 6}{3x}}}$

SOLUTION:-

$\large\Rightarrow{\sf{\dfrac{y + 6}{x} =\dfrac{y - 6}{3x}}}$

By cross multiplication,

$\large\Rightarrow{\sf{3x(y+6)=x(y-6)}}$

$\large\Rightarrow{\sf{3xy+18x=xy-6x}}$

$\large\Rightarrow{\sf{3xy-xy=-6x-18x}}$

Dividing both sides by 2,

$\large\Rightarrow{\sf{\dfrac{\cancel{2}\:xy}{\cancel{2}}=\dfrac{\cancel{-24}\:x}{\cancel{2}}}}$

$\large\boxed{\therefore{\sf{xy=-12x}}}$

Dividing both sides by x,

$\large\Rightarrow{\sf{\dfrac{\cancel{x}\:y}{\cancel{x}}=\dfrac{-12\:\cancel{x}}{\cancel{x}}}}$

$\large{\green{\underline{\boxed{\therefore{\bf{\green{y=-12}}}}}}}$

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

$\sf{\bigstar\:\:\:\:Solve\:\: for\:\:y\::\dfrac{y+6}{x}=\dfrac{y-6}{3 x}}$

$\underline{\underline{\sf{\maltese\:\:Given}}}$

$\sf{\dfrac{y+6}{x}=\dfrac{y-6}{3 x}}$

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Value of y

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

$\boxed{\bf{y=-12}}$

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

$\sf{\dfrac{y+6}{x}=\dfrac{y-6}{3 x}}$

$\bf{\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\dfrac{a}{b}=\dfrac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c}$

$\sf{\implies 3yx+18x=yx-6x}$

$\bf{Subtract\:18x\:from\:both\:sides}$

$\sf{\implies 3yx+18x-18x=yx-6x-18x}$

$\sf{\implies 3yx=yx-24x}$

$\bf{Subtract\:yx\:from\:both\:sides}$

$\sf{\implies 3yx-yx=yx-24x-yx}$

$\sf{\implies 2yx=-24}$

$\bf{Divide\:both\:sides\:by\:2x}$

$\sf{\implies\displaystyle\frac{2yx}{2x}=\frac{-24x}{2x}}$

$\boxed{\bf{y=-12}}$