Question

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Answer 1

1st Answer

$\sf \dashrightarrow 2x + 3y = 5 \: \: --- (i)$

$\sf \dashrightarrow 3x - 2y = 1 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 2x + 3y = 5$

$\sf \dashrightarrow 2x = 5 - 3y$

$\sf \dashrightarrow x = \dfrac{5 - 3y}{2}$

Now, we can find the value of y.

$\sf \dashrightarrow 3x - 2y = 1$

$\sf \dashrightarrow 3 \bigg( \dfrac{5 - 3y}{2} \bigg) - 2y = 1$

$\sf \dashrightarrow \dfrac{15 - 9y}{2} - 2y = 1$

$\sf \dashrightarrow \dfrac{15 - 9y - 4y}{2} = 1$

$\sf \dashrightarrow \dfrac{15 - 13y}{2} = 1$

$\sf \dashrightarrow 15 - 13y = 1 \times 2$

$\sf \dashrightarrow 15 - 13y = 2$

$\sf \dashrightarrow -13y = 2 - 15$

$\sf \dashrightarrow -13y = -13$

$\sf \dashrightarrow y = \dfrac{-13}{-13}$

$\sf \dashrightarrow y = 1$

Now, let's find the value of x.

$\sf \dashrightarrow 2x + 3y = 5$

$\sf \dashrightarrow 2x + 3(1) = 5$

$\sf \dashrightarrow 2x + 3 = 5$

$\sf \dashrightarrow 2x = 5 - 3$

$\sf \dashrightarrow 2x = 2$

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

$\sf \dashrightarrow x = 1$

Hence, the value of x is 1. Thus, option D is the correct answer.

2nd Answer

$\sf \dashrightarrow 3x + 5y = 6 \: \: --- (i)$

$\sf \dashrightarrow 2x + 10y = 8 \: \: --- (ii)$

Now, by first equation,

$\sf \dashrightarrow 3x + 5y = 6$

$\sf \dashrightarrow 3x = 6 - 5y$

$\sf \dashrightarrow x = \dfrac{6 - 5y}{3}$

Now, let's find the value of y.

$\sf \dashrightarrow 2x + 10y = 8$

$\sf \dashrightarrow 2 \bigg( \dfrac{6 - 5y}{3} \bigg) + 10y = 8$

$\sf \dashrightarrow \dfrac{12 - 10y}{3} + 10y = 8$

$\sf \dashrightarrow \dfrac{12 - 10y + 30y}{3} = 8$

$\sf \dashrightarrow \dfrac{12 + 20y}{3} = 8$

$\sf \dashrightarrow 12 + 20y = 8 \times 3$

$\sf \dashrightarrow 12 + 20y = 24$

$\sf \dashrightarrow 20y = 24 - 12$

$\sf \dashrightarrow 20y = 12$

$\sf \dashrightarrow y = \dfrac{12}{20}$

$\sf \dashrightarrow y = \dfrac{3}{5}$

Hence, the value of y is 3/5. Thus, option B is the correct answer.