Question

2x - 5y = 9
3x + 4y = 2​

Answer 1

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

$\rm \: \: \: \: 2x - 5y = 9.... \: (i)$

$\rm \: \: \: 3x + 4y = 2 \: .....(ii)$

$\rm \: Multiply \: eq(i) \: by \: 3$

$\rm \: and$

$\rm \: eq(ii) \: by \: 2$

$\rm \: Now \: new \: equations \: would \: be$

$\longrightarrow \rm \: 6x - 15y = 27 \: ....(iii)$

$\longrightarrow \rm \: 6x + 8y = 4 \: ....(iv)$

$\rm \: Now,$

$\rm \: eq(iii) - eq(iv)$

$\mapsto \rm \: 6x - 15y - (6x + 8y)= 27 - 4$

$\mapsto \: \rm \: 6x - 15y - 6x - 8y = 23$

$\mapsto \rm \: \: - 23y = 23$

$\mapsto \boxed{ \rm{y = - 1}}$

$Now,$

$\rm \: put \: the \: value \: of \: y \: in \: eq(i)$

$\mapsto \rm \: 2x - 5( - 1) = 9$

$\mapsto \rm \: 2x + 5 = 9$

$\mapsto \: \rm \: 2x = 9 - 5$

$\mapsto \: \rm \: 2x = 4$

$\mapsto \boxed{ \rm{x = 2}}$

Answer 2

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

$\rm \: \: \: \: 2x - 5y = 9.... \: (i)$

$\rm \: \: \: 3x + 4y = 2 \: .....(ii)$

$\rm \: multiply \: eq(i) \: by \: 3$

$\rm \: and$

$\rm \: eq(ii) \: by \: 2$

$\rm \: now \: new \: equations \: would \: be$

$\longrightarrow \rm \: 6x - 15y = 27 \: ....(iii)$

$\longrightarrow \rm \: 6x + 8y = 4 \: ....(iv)$

$\rm \: now$

$\rm \: eq(iii) - eq(iv)$

$\mapsto \rm \: 6x - 15y - (6x + 8y)= 27 - 4$

$\mapsto \: \rm \: 6x - 15y - 6x - 8y = 23$

$\mapsto \rm \: \: - 23y = 23$

$\mapsto \boxed{ \rm{y = - 1}}$

${\rm{Now,}}$

$\rm \: put \: the \: value \: of \: y \: in \: eq(i)$

$\mapsto \rm \: 2x - 5( - 1) = 9$

$\mapsto \rm \: 2x + 5 = 9$

$\mapsto \: \rm \: 2x = 9 - 5$

$\mapsto \: \rm \: 2x = 4$

$\mapsto \boxed{ \rm{x = 2}}$