Question

x/3+y/2=4, x/2+y/4=4​

Answer 1

Answer

$\sf \dashrightarrow \dfrac{x}{3} + \dfrac{y}{2} = 4 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{x}{2} + \dfrac{y}{4} = 4 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{x}{3} + \dfrac{y}{2} = 4$

$\sf \dashrightarrow \dfrac{2x + 3y}{6} = 4$

$\sf \dashrightarrow 2x + 3y = 4 \times 6$

$\sf \dashrightarrow 2x + 3y = 24$

By second equation,

$\sf \dashrightarrow \dfrac{x}{2} + \dfrac{y}{4} = 4$

$\sf \dashrightarrow \dfrac{2x + y}{4} = 4$

$\sf \dashrightarrow 2x + y = 4 \times 4$

$\sf \dashrightarrow 2x + y = 16$

Now, again by first new equation,

$\sf \dashrightarrow 2x + 3y = 24$

$\sf \dashrightarrow 2x = 24 - 3y$

$\sf \dashrightarrow x = \dfrac{24 - 3y}{2}$

Now, let's find the value of y by second new equation.

$\sf \dashrightarrow 2x + y = 16$

$\sf \dashrightarrow 2 \bigg( \dfrac{24 - 3y}{2} \bigg) + y = 16$

$\sf \dashrightarrow \dfrac{48 - 6y}{2} + y = 16$

$\sf \dashrightarrow \dfrac{48 - 6y + 2y}{2} = 16$

$\sf \dashrightarrow \dfrac{48 - 4y}{2} = 16$

$\sf \dashrightarrow 48 - 4y = 16 \times 2$

$\sf \dashrightarrow 48 - 4y = 32$

$\sf \dashrightarrow -4y = 32 - 48$

$\sf \dashrightarrow -4y = -16$

$\sf \dashrightarrow y = \dfrac{-16}{-4}$

$\sf \dashrightarrow y = 4$

Now, let's find the value of x by first new equation.

$\sf \dashrightarrow 2x + 3y = 24$

$\sf \dashrightarrow 2x + 3(4) = 24$

$\sf \dashrightarrow 2x + 12 = 24$

$\sf \dashrightarrow 2x = 24 - 12$

$\sf \dashrightarrow 2x = 12$

$\sf \dashrightarrow x = \dfrac{12}{2}$

$\sf \dashrightarrow x = 6$

Hence, the values of x and y are 6 and 4 respectively.