Question

Solve the following pair of linear equation by substitution method 3x+2y=14,x-4y+7=0

Answer 1

Answer

$\sf \dashrightarrow 3x + 2y = 14 \: \: --- (i)$

$\sf \dashrightarrow x - 4y + 7 = 0 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow 3x + 2y = 14$

$\sf \dashrightarrow 3x = 14 - 2y$

$\sf \dashrightarrow x = \dfrac{14 - 2y}{3}$

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

$\sf \dashrightarrow x - 4y + 7 = 0$

$\sf \dashrightarrow x - 4y = -7$

$\sf \dashrightarrow \dfrac{14 - 2y}{3} - 4y = -7$

$\sf \dashrightarrow \dfrac{14 - 2y - 12y}{3} = -7$

$\sf \dashrightarrow \dfrac{14 - 14y}{3} = -7$

$\sf \dashrightarrow 14 - 14y = -7 \times 3$

$\sf \dashrightarrow 14 - 14y = -21$

$\sf \dashrightarrow -14y = -21 - 14$

$\sf \dashrightarrow -14y = -35$

$\sf \dashrightarrow y = \dfrac{-35}{-14}$

$\sf \dashrightarrow y = \dfrac{5}{2}$

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

$\sf \dashrightarrow 3x + 2y = 14$

$\sf \dashrightarrow 3x + 2 \bigg( \dfrac{5}{2} \bigg) = 14$

$\sf \dashrightarrow 3x + \dfrac{10}{2} = 14$

$\sf \dashrightarrow 3x + 5 = 14$

$\sf \dashrightarrow 3x = 14 - 5$

$\sf \dashrightarrow 3x = 9$

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

$\sf \dashrightarrow x = 3$

Hence, the values of x and y are 3 and $\sf \dfrac{5}{2}$ respectively.