Question

solve x/7 +y/3=5 x/2-y/9=6 by substitution method​

Answer 1

Answer

$\sf \dashrightarrow \dfrac{x}{7} + \dfrac{y}{3} = 5 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{x}{2} - \dfrac{y}{9} = 6 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{x}{7} + \dfrac{y}{3} = 5$

$\sf \dashrightarrow \dfrac{3x + 7y}{21} = 5$

$\sf \dashrightarrow 3x + 7y = 21 \times 5$

$\sf \dashrightarrow 3x + 7y = 105$

$\sf \dashrightarrow 3x = 105 - 7y$

$\sf \dashrightarrow x = \dfrac{105 - 7y}{3}$

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

$\sf \dashrightarrow \dfrac{\dfrac{105 - 7y}{3}}{2} - \dfrac{y}{9} = 6$

$\sf \dashrightarrow \dfrac{105 - 7y}{3} \times \dfrac{1}{2} - \dfrac{y}{9} = 6$

$\sf \dashrightarrow \dfrac{105 - 7y}{6} - \dfrac{y}{9} = 6$

$\sf \dashrightarrow \dfrac{945 - 63y - 6y}{54} = 6$

$\sf \dashrightarrow \dfrac{945 - 69y}{54} = 6$

$\sf \dashrightarrow 945 - 69y = 54 \times 6$

$\sf \dashrightarrow 945 - 69y = 324$

$\sf \dashrightarrow -69y = 324 - 945$

$\sf \dashrightarrow -69y = -621$

$\sf \dashrightarrow y = \dfrac{-621}{-69}$

$\sf \dashrightarrow y = 9$

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

$\sf \dashrightarrow \dfrac{x}{7} + \dfrac{y}{3} = 5$

$\sf \dashrightarrow \dfrac{x}{7} + \dfrac{9}{3} = 5$

$\sf \dashrightarrow \dfrac{x}{7} + 3 = 5$

$\sf \dashrightarrow \dfrac{x}{7} = 5 - 3$

$\sf \dashrightarrow \dfrac{x}{7} = 2$

$\sf \dashrightarrow x = 7 \times 2$

$\sf \dashrightarrow x = 14$

Hence, the values of x and y are 14 and 9 respectively.