Question

if 6x+3y=7xy and 3x+9y=11xy then find x+2y

Answer 1

S O L U T I O N :

We have two equation given;

• 6x + 3y = 7xy..............(1)
• 3x + 9y = 11xy.............(2)

$\underline{\mathcal{USING\:\:BY\:\:SUBSTITUTION\:\:METHOD\::}}$

From equation (1),we get;

$\mapsto\tt{6x + 3y = 7xy}$

$\mapsto\tt{\dfrac{6x + 3y}{xy} = 7}$

$\mapsto\tt{\dfrac{6\cancel{x} }{\cancel{x}y} + \dfrac{3\cancel{y}}{x\cancel{y}} = 7}$

$\mapsto\tt{\dfrac{6}{y} + \dfrac{3}{x} =7....................(3)}$

&

From equation (2),we get;

$\mapsto\tt{3x + 9y = 11xy}$

$\mapsto\tt{\dfrac{3x + 9y}{xy} = 11}$

$\mapsto\tt{\dfrac{3\cancel{x} }{\cancel{x}y} + \dfrac{9\cancel{y}}{x\cancel{y}} = 11}$

$\mapsto\tt{\dfrac{3}{y} + \dfrac{9}{x} =11....................(4)}$

Let suppose 1/y = r & 1/x = m :

$\bullet\sf{6r + 3m = 7...............(5)}$

$\bullet\sf{3r + 9m =11.............(6)}$

From equation (5),we get;

$\mapsto\tt{6r + 3m = 7}$

$\mapsto\tt{6r = 7 - 3m}$

$\mapsto\tt{r=\dfrac{7-3m}{6} .............(7)}$

∴ Putting the value of r in equation (6),we get;

$\mapsto\tt{3\bigg(\dfrac{7-3m}{6} \bigg) +9m = 11}$

$\mapsto\tt{\dfrac{21-9m}{6} +9m = 11}$

$\mapsto\tt{21- 9m + 54m = 66}$

$\mapsto\tt{21+45m = 66}$

$\mapsto\tt{45m = 66 - 21}$

$\mapsto\tt{45m = 45}$

$\mapsto\tt{m = \cancel{45/45}}$

$\mapsto\bf{m = 1}$

∴ Putting the value of m in equation (7),we get;

$\mapsto\tt{r=\dfrac{7-3(1)}{6}}$

$\mapsto\tt{r=\dfrac{7-3}{6}}$

$\mapsto\tt{r=\cancel{\dfrac{4}{6}}}$

$\mapsto\bf{r = 2/3}$

Now,

→ 1/y = r

→ 1/y = 2/3

→ 2y = 3

→ y = 3/2

Or

→ 1/x = m

→ 1/x = 1

→ x = 1

According to the question :

⇒ x + 2y

⇒ 1 + 2 × 3/2

⇒ 1 + 6/2

⇒ 1 + 3

⇒ 4