Question

2□-4/□=10. 2□+2/□=4​

Answer 1

1. 2(3)-4/(-1) = 10
2. 2(3)+2/(-1)= 4
3. (3)-(-1)= 4

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Answer 2

$\purple{\large{\underline{\underline{ \rm{Given: }}}}}$

$\sf2 \: □ - \dfrac{4}{□} = 10$

$\sf2 \: □ - \dfrac{2}{□} = 4$

$\sf □ - \: □ = ?$

$\purple{\large{\underline{\underline{ \rm{To \: Find: }}}}}$

Values which can replace faces.

$\purple{\large{\underline{\underline{ \rm{Solution: }}}}}$

Let,

◈ The girl's face = x

◈ The boy's face = y

Then we have:

$\sf2x - \dfrac{4}{y} = 10$ .......①

$\sf2x + \dfrac{2}{y} = 4$ .......②

Subtract eq① from eq②, we have:

$\sf2x + \dfrac{2}{y} - (2x - \dfrac{4}{y} )= 4 - 10$

$\sf{ \implies{ \dfrac{2xy + 2}{y} - ( \dfrac{2xy - 4}{y} ) = - 6}}$

$\sf{ \implies{\dfrac{(2xy + 2) - (2xy - 4)}{y} = - 6}}$

$\sf{ \implies{ \dfrac{2xy + 2 - 2xy + 4}{y} = - 6}}$

$\sf{ \implies{ \dfrac{2 + 4}{y} = - 6}}$

$\sf{ \implies{ \dfrac{6}{y} = - 6}}$

$\sf{ \implies{6 = - 6y}}$

$\sf{ \implies{ - \dfrac{6}{6} = y}}$

$\sf{ \implies{y = - 1}}$

∴ Boy's face i.e.,

$\sf{ \blue{ \underline{ \boxed{ \sf{y = - 1}}}}}$

Put the value of y in eq① to get the value of x

$\sf{2x - \dfrac{4}{y} = 10}$

$\sf{ \implies{2x - ( - \dfrac{4}{1} ) = 10}}$

$\sf{ \implies{2x + 4 = 10}}$

$\sf{ \implies{2x = 10 - 4}}$

$\sf{ \implies{2x = 6}}$

$\sf{ \implies{x = \dfrac{6}{2}}}$

$\sf{ \implies{x = 3}}$

∴ Girl's face i.e.,

$\sf{ \blue{ \underline{ \boxed{ \sf{x = 3}}}}}$

Now,

$\sf{x - y = \: ? }$

Substitute the values of x and y, we have:

$\sf{3 - ( - 1)}$

$\sf = {3 + 1}$

$\sf = 4$

$\sf{ \therefore{ \blue{ \underline{ \boxed{ \sf{3 - ( - 1) = 4}}}}}}$

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$\sf{ \purple{Let's \: Verify \: it :-}}$

Case 1 :-

$\sf2(3) - ( - \dfrac{4}{1} )$

$\sf = 6 + 4$

$\sf = 10$

Case 2 :-

$\sf2(3) + ( - \dfrac{2}{1} )$

$\sf = 6 - 2$

$\sf = 4$

Case 3 :-

$\sf3 - ( - 1)$

$\sf = 3 + 1$

$\sf = 4$

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