Question

Answere must be
x = 2 , y = 3
I NEED FULL SOLUTION​

Answer 1

Answer:

$\frac{{ (\sqrt{32}) }^{x} }{ {2}^{y + 1} } = 1 \\ {( \sqrt{32}) }^{x} = {2}^{y + 1} \\ {( ({ {2}^{5} )}^{ \frac{1}{2} }) }^{x} = {2}^{y + 1} \\ {2}^{ \frac{5x}{2} } = {2}^{y + 1} \\ \blue{\mathfrak{\underline{\large{On \: comparing}}}:} \\ \frac{5x}{2} = y + 1 \\ 5x = 2y + 2 \\ 5x - 2y = 2 - (i) \\ \\ {16}^{4 - \frac{x}{2} } - {8}^{y} = 0 \\ {16}^{4 - \frac{x}{2} } = {8}^{y} \\ { ({2}^{4} )}^{ \frac{8 - x}{2} } = { ({2}^{3} )}^{y} \\ {2}^{16 - 2x} = {2}^{3y} \\ \blue{\mathfrak{\underline{\large{On \: comparing}}}:} \\ 16 - 2x = 3y \\ 2x + 3y = 16 - (ii) \\ \blue{\mathfrak{\underline{\large{multiply \: {eq}^{n} \: (i)by \: 2 \: and \: (ii) by \: 5}}}:} \\ 10x - 4y = 4 - (iii) \\ 10x + 15y = 80 - (iv) \\\blue{\mathfrak{\underline{\large{Subtract \: {eq}^{n} \:(iii) \: in \: (iv) }}}:} \\ 10x + 15y = 80 \\ 10x \: - \: \: 4y = 4 \: \: \\ - \: \: \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \\ - - - - - - - - - \\ 19y = 76 \\ \boxed{y = 4} \\\blue{\underline{\large{Put \: the \: value \: of \: y \: in \: {eq}^{n} \: (i)}} : } \\ 5x - 8 = 2 \\ 5x = 10 \\ \boxed{x = 2} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$