Question

x upon 3 + y upon 4=5 & x upon 2 + y upon 3=7 by subsitution metod​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

$\sf{\dfrac{x}{3} +\dfrac{y}{4} =5\:\:\:\:\:\:\:\& \:\:\:\:\:\dfrac{x}{2} +\dfrac{y}{3} =7}$

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The value of x and y.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

$\bullet\sf{\dfrac{x}{3} +\dfrac{y}{4} =5..........................(1)}\\\\\bullet\sf{\dfrac{x}{2} +\dfrac{y}{3} =7..........................(2)}$

$\underline{\underline{\bf{Using\:Substitution\:Method\::}}}}}$

From equation (1),we get;

$\longrightarrow\sf{\dfrac{x}{3} +\dfrac{y}{4} =5}\\\\\\\longrightarrow\sf{\dfrac{4x+3y}{12} =5}\\\\\\\longrightarrow\sf{4x+3y=60}\\\\\\\longrightarrow\sf{4x=60-3y}\\\\\\\longrightarrow\sf{x=\dfrac{60-3y}{4} ......................(3)}$

Putting the value of x in equation (2),we get;

$\longrightarrow\sf{\dfrac{x}{2} +\dfrac{y}{3} =7}\\\\\\\longrightarrow\sf{\dfrac{3x+2y}{6} =7}\\\\\\\longrightarrow\sf{3x+2y=42}\\\\\\\longrightarrow\sf{3\bigg(\dfrac{60-3y}{4} \bigg)+2y=42}\\\\\\\longrightarrow\sf{\dfrac{180-9y}{4} +2y=42}\\\\\\\longrightarrow\sf{180-9y+8y=168}\\\\\\\longrightarrow\sf{180-y=168}\\\\\\\longrightarrow\sf{-y=168-180}\\\\\\\longrightarrow\sf{\cancel{-}y=\cancel{-}12}\\\\\\\longrightarrow\sf{\pink{y=12}}$

Putting the value of y in equation (3),we get;

$\longrightarrow\sf{x=\dfrac{60-3y}{4} }\\\\\\\longrightarrow\sf{x=\dfrac{60-3(12)}{4} }\\\\\\\longrightarrow\sf{x=\dfrac{60-36}{4} }\\\\\\\longrightarrow\sf{x=\cancel{\dfrac{24}{4} }}\\\\\\\longrightarrow\sf{\pink{x=6}}$

Thus;

The value of x is 6 and y is 12 .

Answer 2

Given:

x/3 + y/4 = 5 & x/2 + y/3 = 7

To find:

The value of x and y.

Explanation:

• x/3 + y/4 = 5.............(1)

• x/2 + y/3 = 7.............(2)

using substitution method:

from equation (1), we get;

x/3 + y/4 = 5

4x + 3y = 60

4x = 60 - 3y

x = 60 - 3y / 4............(3)

putting the value of x in equation (2), we get;

x/2 + y/3 = 7

3x + 2y /6 = 7

3x + 2y = 42

3(60 + 3y /4 ) + 2y = 42

180 - 9y / 4 + 2y = 42

180 - 9y + 8y = 168

-y = 168 - 180

-y = -12

y = 12

putting the value of y in equation (3), we get;

x = 60 - 3y / 4

x = 60 - 3(12) / 4

x = 60 - 36 / 4

x = 24/4

x = 6

Thus, the value of x is 6 and y is 12.

silentlover45.❤️