Question

Solve the pair of linear equations by substitution method.

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Answer 1

Answer

$\sf \dashrightarrow 9x + 3y = 25 \: \: --- (i)$

$\sf \dashrightarrow 14x + 13y = 95 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 9x + 3y = 25$

$\sf \dashrightarrow 9x = 25 - 3y$

$\sf \dashrightarrow x = \dfrac{25 - 3y}{9}$

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

$\sf \dashrightarrow 14x + 13y = 95$

$\sf \dashrightarrow 14 \bigg( \dfrac{25 - 3y}{9} \bigg) + 13y = 95$

$\sf \dashrightarrow \dfrac{350 - 42y}{9} + 13y = 95$

$\sf \dashrightarrow \dfrac{350 - 42y + 117y}{9} = 95$

$\sf \dashrightarrow \dfrac{350 + 75y}{9} = 95$

$\sf \dashrightarrow 350 + 75y = 95 \times 9$

$\sf \dashrightarrow 350 + 75y = 855$

$\sf \dashrightarrow 75y = 885 - 350$

$\sf \dashrightarrow 75y = 505$

$\sf \dashrightarrow y = \dfrac{505}{75}$

$\sf \dashrightarrow y = \dfrac{101}{15}$

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

$\sf \dashrightarrow 9x + 3y = 25$

$\sf \dashrightarrow 9x + 3 \bigg( \dfrac{101}{15} \bigg) = 25$

$\sf \dashrightarrow 9x + \dfrac{101}{3} = 25$

$\sf \dashrightarrow 9x = 25 - \dfrac{101}{3}$

$\sf \dashrightarrow 9x = \dfrac{75 - 101}{3}$

$\sf \dashrightarrow 9x = \dfrac{-26}{3}$

$\sf \dashrightarrow x = \dfrac{\dfrac{-26}{3}}{9}$

$\sf \dashrightarrow x = \dfrac{-26}{3} \times \dfrac{1}{9}$

$\sf \dashrightarrow x = \dfrac{-26}{27}$

Hence, the values of x and y are $\sf \dfrac{-26}{27}$ and $\sf \dfrac{101}{15}$ respectively.