Question

5x-4y+8=0,7x+6y-9=0​

Answer 1

${ \sf{ \large{ the \: given \: equations \: are \longrightarrow}}}$

${ \rm{5x - 4y + 8 = 0 \longrightarrow(i)}}$

${ \rm{7x - 6y - 9 = 0 \longrightarrow(ii)}}$

${ \sf{ \large{ taking \: eq.(i) \longrightarrow}}}$

${ \rm{5x - 4y + 8 = 0 }}$

${ \rm{ \implies5x = 4y - 8 }}$

${ \rm{ \implies \: x = \dfrac{4y - 8}{5} }}$

${ \sf{ \large{ taking \: eq.(ii) \longrightarrow}}}$

${ \rm{7x - 6y - 9 = 0}}$

${ \rm{ \implies7( \dfrac{4y - 8}{5}) - 6y - 9 = 0}}$

${ \rm{ \implies\dfrac{28y - 56}{5} - 6y - 9 = 0}}$

${ \rm{ \implies{28y - 56} - 6y =9 \times 5}}$

${ \rm{ \implies22y =45 + 56}}$

${ \rm{ \implies22y =101}}$

${ \rm{ \implies y = \dfrac{101}{22}}}$

${ \rm{ \implies y = 4.5}}$

${ \sf{ \large{ taking \: eq.(i) \longrightarrow}}}$

${ \rm{5x - 4y + 8 = 0 }}$

${ \rm{ \implies5x - 4(4.5)+ 8 = 0 }}$

${ \rm{ \implies5x - 18+ 8 = 0 }}$

${ \rm{ \implies5x = 18 - 8 }}$

${ \rm{ \implies \: x = \dfrac{10}{5} }}$

${ \rm{ \implies \: x = \dfrac{ { \not10}^{2} }{ \not5} }}$

${ \rm{x = 5}}$

${ \tt{ \large{ the \: value \: of \colon}}}$

${ \tt{ \large{x = 4.5}}}$

${ \tt{ \large{y = 2}}}$