Question

x/5 + y/6 =9/10 ; x/6 + y/5 = 14/15 in substitution method​

Answer 1

Answer

$\sf \dashrightarrow \dfrac{x}{5} + \dfrac{y}{6} = \dfrac{9}{10} \: \: --- (i)$

$\sf \dashrightarrow \dfrac{x}{6} + \dfrac{y}{5} = \dfrac{14}{15} \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{x}{5} + \dfrac{y}{6} = \dfrac{9}{10}$

$\sf \dashrightarrow \dfrac{x}{5} = \dfrac{9}{10} - \dfrac{y}{6}$

$\sf \dashrightarrow \dfrac{x}{5} = \dfrac{54 - 10y}{60}$

$\sf \dashrightarrow x = 5 \bigg( \dfrac{54 - 10y}{60} \bigg) = \dfrac{270 - 50y}{60}$

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

$\sf \dashrightarrow \dfrac{x}{6} + \dfrac{y}{5} = \dfrac{14}{15}$

$\sf \dashrightarrow \dfrac{\dfrac{270 - 50y}{60}}{6} + \dfrac{y}{5} = \dfrac{14}{15}$

$\sf \dashrightarrow \dfrac{270 - 50y}{60} \times \dfrac{1}{6} + \dfrac{y}{5} = \dfrac{14}{15}$

$\sf \dashrightarrow \dfrac{270 - 50y}{360} + \dfrac{y}{5} = \dfrac{14}{15}$

$\sf \dashrightarrow \dfrac{270 - 50y + 72y}{360} = \dfrac{14}{15}$

$\sf \dashrightarrow \dfrac{270 + 22y}{360} = \dfrac{14}{15}$

$\sf \dashrightarrow 15 (270 + 22y) = 14 (360)$

$\sf \dashrightarrow 4050 + 330y = 5040$

$\sf \dashrightarrow 330y = 5040 - 4050$

$\sf \dashrightarrow 330y = 990$

$\sf \dashrightarrow y = \dfrac{990}{330}$

$\sf \dashrightarrow y = 3$

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

$\sf \dashrightarrow \dfrac{x}{5} + \dfrac{y}{6} = \dfrac{9}{10}$

$\sf \dashrightarrow \dfrac{x}{5} + \dfrac{3}{6} = \dfrac{9}{10}$

$\sf \dashrightarrow \dfrac{x}{5} + \dfrac{1}{2} = \dfrac{9}{10}$

$\sf \dashrightarrow \dfrac{2x + 5}{10} = \dfrac{9}{10}$

$\sf \dashrightarrow 10 (2x + 5) = 10 (9)$

$\sf \dashrightarrow 20x + 50 = 90$

$\sf \dashrightarrow 20x = 90 - 50$

$\sf \dashrightarrow 20x = 40$

$\sf \dashrightarrow x = \dfrac{40}{20}$

$\sf \dashrightarrow x = 2$

Hence, the values of x and y are 2 and 3 respectively.