Question

2x+1/7+5y-3/3 =12 and3x+2/2-4y+3/6=13 solve by substitution

Answer 1

Answer

$\sf \dashrightarrow \dfrac{2x + 1}{7} + \dfrac{5y - 3}{3} = 12 \: \: --- (i)$

$\sf \dashrightarrow \dfrac{3x + 2}{2} - \dfrac{4y + 3}{6} = 13 \: \: --- (ii)$

By first equation,

$\sf \dashrightarrow \dfrac{2x + 1}{7} + \dfrac{5y - 3}{3} = 12$

$\sf \dashrightarrow \dfrac{6x + 3}{21} + \dfrac{35y - 21}{21} = 12$

$\sf \dashrightarrow \dfrac{6x + 3 + 35y - 21}{21} = 12$

$\sf \dashrightarrow \dfrac{6x + 35y - 18}{21} = 12$

$\sf \dashrightarrow 6x + 35y - 18 = 21 \times 12$

$\sf \dashrightarrow 6x + 35y - 18 = 252$

$\sf \dashrightarrow 6x + 35y = 252 + 18$

$\sf \dashrightarrow 6x + 35y = 270 \: \: --- (iii)$

By second equation,

$\sf \dashrightarrow \dfrac{3x + 2}{2} - \dfrac{4y + 3}{6} = 13$

$\sf \dashrightarrow \dfrac{9x + 6}{6} - \dfrac{4y + 3}{6} = 13$

$\sf \dashrightarrow \dfrac{9x + 6 - 4y + 3}{6} = 13$

$\sf \dashrightarrow \dfrac{9x - 4y + 9}{6} = 13$

$\sf \dashrightarrow 9x - 4y + 9 = 13 \times 6$

$\sf \dashrightarrow 9x - 4y + 9 = 78$

$\sf \dashrightarrow 9x - 4y = 78 - 9$

$\sf \dashrightarrow 9x - 4y = 69 \: \: --- (iv)$

By third equation,

$\sf \dashrightarrow 6x + 35y = 270$

$\sf \dashrightarrow 6x = 270 - 35y$

$\sf \dashrightarrow x = \dfrac{270 - 35y}{6}$

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

$\sf \dashrightarrow 9x - 4y = 69$

$\sf \dashrightarrow 9 \bigg( \dfrac{270 - 35y}{6} \bigg) - 4y = 69$

$\sf \dashrightarrow \dfrac{2430 - 315y}{6} - 4y = 69$

$\sf \dashrightarrow \dfrac{2460 - 315y - 24y}{6} = 69$

$\sf \dashrightarrow \dfrac{2460 - 339y}{6} = 69$

$\sf \dashrightarrow 2460 - 339y = 69 \times 6$

$\sf \dashrightarrow 2460 - 339y = 414$

$\sf \dashrightarrow -339y = 414 - 2460$

$\sf \dashrightarrow -339y = -2046$

$\sf \dashrightarrow y = \dfrac{-2046}{-339}$

$\sf \dashrightarrow y = \dfrac{682}{113}$

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

$\sf \dashrightarrow 6x + 35y = 270$

$\sf \dashrightarrow 6x + 35 \bigg( \dfrac{682}{113} \bigg) = 270$

$\sf \dashrightarrow 6x + \dfrac{23870}{113} = 270$

$\sf \dashrightarrow 6x = 270 - \dfrac{23870}{113}$

$\sf \dashrightarrow 6x = \dfrac{30510 - 23870}{113}$

$\sf \dashrightarrow 6x = \dfrac{6640}{113}$

$\sf \dashrightarrow x = \dfrac{\dfrac{6640}{113}}{6}$

$\sf \dashrightarrow x = \dfrac{6640}{113} \times \dfrac{1}{6}$

$\sf \dashrightarrow x = \dfrac{6640}{678}$

$\sf \dashrightarrow x = \dfrac{3320}{389}$

Hence, the values of x and y are $\sf \dfrac{3320}{389}$ and $\sf \dfrac{682}{113}$ respectively.