Question

solve the given simultaneous equations:
x/3+y/4=4 ; x/2-y/4=1​

Answer 1

Answer

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

$\sf \dashrightarrow \dfrac{x}{2} - \dfrac{y}{4} = 1 \: \: --- (ii)$

By first equation,

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

$\sf \dashrightarrow \dfrac{4x + 3y}{12} = 4$

$\sf \dashrightarrow 4x + 3y = 12 \times 4$

$\sf \dashrightarrow 4x + 3y = 48 \: \: --- (iii)$

By second equation,

$\sf \dashrightarrow \dfrac{x}{2} - \dfrac{y}{4} = 1$

$\sf \dashrightarrow \dfrac{2x - y}{4} = 1$

$\sf \dashrightarrow 2x - y = 4 \times 1$

$\sf \dashrightarrow 2x - y = 4 \: \: --- (iv)$

By third equation,

$\sf \dashrightarrow 4x + 3y = 48$

$\sf \dashrightarrow 4x = 48 - 3y$

$\sf \dashrightarrow x = \dfrac{48 - 3y}{4}$

Now, we can find the value of y by fourth equation.

$\sf \dashrightarrow 2x - y = 4$

$\sf \dashrightarrow 2 \bigg( \dfrac{48 - 3y}{4} \bigg) - y = 4$

$\sf \dashrightarrow \dfrac{96 - 6y}{4} - y = 4$

$\sf \dashrightarrow \dfrac{96 - 6y - 4y}{4} = 4$

$\sf \dashrightarrow \dfrac{96 - 10y}{4} = 4$

$\sf \dashrightarrow 96 - 10y = 4 \times 4$

$\sf \dashrightarrow 96 - 10y = 16$

$\sf \dashrightarrow -10y = 16 - 96$

$\sf \dashrightarrow -10y = -80$

$\sf \dashrightarrow y = \dfrac{-80}{-10}$

$\sf \dashrightarrow y = 8$

Now, we can find the value of x by third equation.

$\sf \dashrightarrow 4x + 3y = 48$

$\sf \dashrightarrow 4x + 3(8) = 48$

$\sf \dashrightarrow 4x + 24 = 48$

$\sf \dashrightarrow 4x = 48 - 24$

$\sf \dashrightarrow 4x = 24$

$\sf \dashrightarrow x = \dfrac{24}{4}$

$\sf \dashrightarrow x = 6$

Hence, the values of x and y are 6 and 8 respectively.