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

1.	17x+23y=40 & 23x+17y=100 so x-y =?
Answer» $\underline{\pink{\bf{Given}}}\\$ ${ \sf17x + 23y = 40}\\$ ${ \sf23x + 17y = 100}\\$ $\underline{\pink{\bf{To~Find}}}\\\\$ $\sf \: x - y\\$ $\\\underline{\pink{\bf{Solution}}}\\$ We have $\\{ \sf17x + 23y = 40} \: \: \: \: \: - - - - (<klux>1</klux>)\\\\$ ${ \sf23x + 17y = 100} \: \: \: \: \: - - - - (2)\\$ On SOLVING EQUATION 1 We GET, $\\{ \implies\sf17x + 23y = 40}$ ${ \implies\sf17x = 40 - 23y}$ ${ \implies\sf x = \cfrac{ 40 - 23y}{17}}\\\\$ $\\\text{\orange{Putting the value of x in Equation 2 We get,}}$ $\\ { \implies\sf23 \left(\cfrac{ 40 - 23y}{17} \right) + 17y = 100}$ ${ \implies\sf\cfrac{ (23 \times 40 )-(23 \times 23y)}{17} + 17y = 100}$ ${ \implies\sf\cfrac{ 920 - 529y}{17} + 17y = 100}$ ${ \implies\sf\cfrac{ 920 - 529y + 289y}{17} = 100}$ ${ \implies\sf\cfrac{ 920 - 240y}{17} = 100}$ ${ \implies\sf920 - 240y = 100 \times 17}$ ${ \implies\sf- 240y =1700 - 920}$ ${ \implies\sf- 240y =780}$ ${ \implies\sf y = \cfrac{ \: \: \xcancel{780}^{3.25} }{ \xcancel{ - 240}}}$ ${~~~~~~~ \green{\sf y = - 3.25}}\\\\$ $\text{\blue{Putting the value of Y in Equation 1 We get,}}\\\\$ ${\implies \sf17x + 23y = 40}$ ${ \implies\sf17x + 23 \times( - 3.25 )= 40}$ ${\implies \sf17x - 74.55= 40}$ ${ \implies\sf17x = 40 + 74.75}$ ${\implies \sf x = \cfrac{40 + 74.75}{17}}$ ${\implies \sf x = \cfrac{114.75}{17}}$ ${ ~~~~~~~\orange{\sf x = 6.75}}\\\\$ $\implies\sf{Value \: of \: (x-y)= 6.75-(-3.25)}$ $\implies\sf{Value \: of \: (x-y)= 6.75 + 3.25}$ $~~~~~~~~~~~~\pink{\underbrace{\underline{\bf{\green{Value \: of \: (x-y)= \huge{10}}}}}}$

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