Solve : 2/x+3/3y =1/6 and 3/x+2/y …

Solve : 2/x+3/3y =1/6 and 3/x+2/y =0

Posted by Riya Singh 4 years, 10 months ago

2 answers

Saraswati Sabat 4 years, 10 months ago

3(2/x +3/3y = 1/6) 2(3/x+2/y = 0) 6/x +3/y = 1/2 6/x +4/y = 0 (-) (-) 0 + (-y) = 1/2 y = -2 2/x - 3/6 = 1/6 2/x = 1/6 + 3/6 2/x = 4/6 4x = 12 x = 3

2Thank You

Rajan Kumar Pasi 4 years, 10 months ago

This is a very simple question of linear equations in two variables chapter, I think you have to practice more on fractions arithmetic.

{tex}\large Question:\frac 2x +\frac 3{3y}=\frac 16\space and\space \frac 3x +\frac 2y=0,\space find\space x,y?{/tex}

Solution:


{tex}\large\implies\boxed {\frac {2\times 3y +3\times x}{x\times 3y}=\frac 16 \space \dots eq.(i)}{/tex} {tex}\large{\implies {\frac {6y +3x}{3xy}=\frac 16 \space }}{/tex} {tex}\large {\underline {Step\space 2:\space Cross-multiplication:} }{/tex} {tex}\large{\implies {6\times{(6y +3x)}=1\times {3xy} \space }}{/tex} {tex}\large{\implies {36y +18x}={3xy} \space }{/tex} {tex}\large{\implies {36y +18x}-{3xy}=0 \space }{/tex}	{tex}\large {\implies\boxed {\frac {3\times y +2\times x}{x\times y}=0 \space\dots eq.(ii) }}{/tex} {tex}\large {\implies\frac {3y +2x}{xy}=0 \space }{/tex} {tex}\large {\underline {Step\space 2:\space Cross-multiplication:} }{/tex} {tex}\large {\implies{3y +2x}=0\times {xy}=0 \space }{/tex} {tex}\large {\implies\boxed {{3y}=-2x \space \dots eq.(iii)}}{/tex}

{tex}\large\implies\boxed {\frac {2\times 3y +3\times x}{x\times 3y}=\frac 16 \space \dots eq.(i)}{/tex}

{tex}\large{\implies {\frac {6y +3x}{3xy}=\frac 16 \space }}{/tex}

{tex}\large {\underline {Step\space 2:\space Cross-multiplication:} }{/tex}

{tex}\large{\implies {6\times{(6y +3x)}=1\times {3xy} \space }}{/tex}

{tex}\large{\implies {36y +18x}={3xy} \space }{/tex}

{tex}\large{\implies {36y +18x}-{3xy}=0 \space }{/tex}

{tex}\large {\implies\boxed {\frac {3\times y +2\times x}{x\times y}=0 \space\dots eq.(ii) }}{/tex}

{tex}\large {\implies\frac {3y +2x}{xy}=0 \space }{/tex}

{tex}\large {\underline {Step\space 2:\space Cross-multiplication:} }{/tex}

{tex}\large {\implies{3y +2x}=0\times {xy}=0 \space }{/tex}

{tex}\large {\implies\boxed {{3y}=-2x \space \dots eq.(iii)}}{/tex}

{tex}\large {\underline {Step\space 3:\space Putting\space relation\space of\space eq.(iii):} }{/tex}

{tex}\large{\implies {{\underline {3y}}(12-x) +18x}=0 \space }{/tex}

{tex}\large{\implies {\underline{(-2x)}(12-x) +18x}=0 \space }{/tex}

{tex}\large{\implies {-24x+2x^2 +18x}=0 \space }{/tex}

{tex}\large{\implies {2x^2-6x}=0 \space }{/tex}

{tex}\large{\implies {2x^2=6x \space} }{/tex}

{tex}\large{\implies\boxed {x=2 \space} }{/tex}

{tex}\large {\underline {Step\space 4:\space Putting\space value\space of\space 'x'\space in\space eq.(iii):} }{/tex}{tex}\large {\implies{3y}=-2x \space }\\ \large {\implies{3y}=-2\times 2 \space }\\ \large\implies\boxed {{y}={-4\over3} \space }\\{/tex}

3Thank You

ANSWER