Question

17x+23y=40 & 23x+17y=100 so x-y =?

Answer 1

$\underline{\pink{\bf{Given}}}$

• ${ \sf17x + 23y = 40}$
• ${ \sf23x + 17y = 100}$

$\underline{\pink{\bf{To~Find}}}$

• $\sf \: x - y$

$\\\underline{\pink{\bf{Solution}}}$

We have

$\\{ \sf17x + 23y = 40} \: \: \: \: \: - - - - (1)$

${ \sf23x + 17y = 100} \: \: \: \: \: - - - - (2)$

On Solving Equation 1 We get,

$\\{ \implies\sf17x + 23y = 40}$

${ \implies\sf17x = 40 - 23y}$

${ \implies\sf x = \cfrac{ 40 - 23y}{17}}$

$\\\text{\orange{Putting the value of x in Equation 2 We get,}}$

$\\ { \implies\sf23 \left(\cfrac{ 40 - 23y}{17} \right) + 17y = 100}$

${ \implies\sf\cfrac{ (23 \times 40 )-(23 \times 23y)}{17} + 17y = 100}$

${ \implies\sf\cfrac{ 920 - 529y}{17} + 17y = 100}$

${ \implies\sf\cfrac{ 920 - 529y + 289y}{17} = 100}$

${ \implies\sf\cfrac{ 920 - 240y}{17} = 100}$

${ \implies\sf920 - 240y = 100 \times 17}$

${ \implies\sf- 240y =1700 - 920}$

${ \implies\sf- 240y =780}$

${ \implies\sf y = \cfrac{ \: \: \xcancel{780}^{3.25} }{ \xcancel{ - 240}}}$

${~~~~~~~ \green{\sf y = - 3.25}}$

$\text{\blue{Putting the value of Y in Equation 1 We get,}}$

${\implies \sf17x + 23y = 40}$

${ \implies\sf17x + 23 \times( - 3.25 )= 40}$

${\implies \sf17x - 74.55= 40}$

${ \implies\sf17x = 40 + 74.75}$

${\implies \sf x = \cfrac{40 + 74.75}{17}}$

${\implies \sf x = \cfrac{114.75}{17}}$

${ ~~~~~~~\orange{\sf x = 6.75}}$

$\implies\sf{Value \: of \: (x-y)= 6.75-(-3.25)}$

$\implies\sf{Value \: of \: (x-y)= 6.75 + 3.25}$

$~~~~~~~~~~~~\pink{\underbrace{\underline{\bf{\green{Value \: of \: (x-y)= \huge{10}}}}}}$