Question

if 5x+6y:8x+5y=8:9, find x:y​

Answer 1

Answer

$\sf \dashrightarrow 5x + 6y = 8 \: \: ---(ii)$

$\sf \dashrightarrow 8x + 5y = 9 \: \: --- (ii)$

By first equations,

$\sf \dashrightarrow 5x + 6y = 8$

$\sf \dashrightarrow 5x = 8 - 6y$

$\sf \dashrightarrow x = \dfrac{8 - 6y}{5}$

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

$\sf \dashrightarrow 8x + 5y = 9$

$\sf \dashrightarrow 8 \bigg( \dfrac{8 - 6y}{5} \bigg) + 5y = 9$

$\sf \dashrightarrow \dfrac{64 - 48y}{5} + 5y = 9$

$\sf \dashrightarrow \dfrac{64 - 48y + 25y}{5} = 9$

$\sf \dashrightarrow \dfrac{64 - 23y}{5} = 9$

$\sf \dashrightarrow 64 - 23y = 9 \times 5$

$\sf \dashrightarrow 64 - 23y = 45$

$\sf \dashrightarrow -23y = 45 - 64$

$\sf \dashrightarrow -23y = -19$

$\sf \dashrightarrow y = \dfrac{-19}{-23}$

$\sf \dashrightarrow y = \dfrac{19}{23}$

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

$\sf \dashrightarrow 5x + 6y = 8$

$\sf \dashrightarrow 5x + 6 \bigg( \dfrac{19}{23} \bigg) = 8$

$\sf \dashrightarrow 5x + \dfrac{114}{23} = 8$

$\sf \dashrightarrow \dfrac{115x + 114}{23} = 8$

$\sf \dashrightarrow 115x + 114 = 8 \times 23$

$\sf \dashrightarrow 115x + 114 = 184$

$\sf \dashrightarrow 115x = 184 - 114$

$\sf \dashrightarrow 115x = 70$

$\sf \dashrightarrow x = \dfrac{70}{115}$

$\sf \dashrightarrow x = \dfrac{14}{23}$

Hence, the values of x and y are $\sf \dfrac{14}{23}$ and $\sf \dfrac{19}{23}$ respectively.