Question

solution for the equation:x+3/4+2y+9/3=3,2x+1/2-y+3/4=4 1/2 is
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Answer 1

★ Solution :-

$\sf \leadsto x + \dfrac{3}{4} + 2y + \dfrac{9}{3} = 3 \: \: - - - (i)$

$\sf \leadsto 2x + \dfrac{1}{2} - y + \dfrac{3}{4} = 4 \dfrac{1}{2} \: \: - - - (ii)$

By first equation,

$\sf \leadsto x + \dfrac{3}{4} + 2y + \dfrac{9}{3} = 3$

$\sf \leadsto x + 2y + \dfrac{9 + 36}{12} = 3$

$\sf \leadsto x + 2y + \dfrac{45}{12} = 3$

$\sf \leadsto x + 2y = 3 - \dfrac{45}{12}$

$\sf \leadsto x + 2y = \dfrac{36 - 45}{12}$

$\sf \leadsto x + 2y = \dfrac{ - 9}{12}$

$\sf \leadsto x + 2y = \dfrac{ - 3}{4} \: \: - - - (iii)$

Now, by second equation,

$\sf \leadsto 2x + \dfrac{1}{2} - y + \dfrac{3}{4} = 4 \dfrac{1}{2}$

$\sf \leadsto 2x - y + \dfrac{3 + 2}{4} = 4 \dfrac{1}{2}$

$\sf \leadsto 2x - y + \dfrac{5}{4} = \dfrac{9}{2}$

$\sf \leadsto 2x - y = \dfrac{9}{2} - \dfrac{5}{4}$

$\sf \leadsto 2x - y = \dfrac{18 - 5}{4}$

$\sf \leadsto 2x - y = \dfrac{13}{4} \: \: - - - (iv)$

Now, by third equation,

$\sf \leadsto x + 2y = \dfrac{ - 3}{4}$

$\sf \leadsto x = \dfrac{ - 3}{4} - 2y$

$\sf \leadsto x = \dfrac{ - 3 - 8y}{4}$

Now, by fourth equation,

$\sf \leadsto 2x - y = \dfrac{13}{4}$

$\sf \leadsto 2 \bigg( \dfrac{ - 3 - 8y}{4} \bigg) - y = \dfrac{13}{4}$

$\sf \leadsto \dfrac{ - 6 - 16y}{4} - y = \dfrac{13}{4}$

$\sf \leadsto \dfrac{ - 6 - 16y - 4y}{4} = \dfrac{13}{4}$

$\sf \leadsto \dfrac{ - 6 - 20y}{4} = \dfrac{13}{4}$

$\sf \leadsto 4( - 6 - 20y) = 4(13)$

$\sf \leadsto - 24 - 80y = 52$

$\sf \leadsto - 80y = 52 + 24$

$\sf \leadsto - 80y = 76$

$\sf \leadsto y = \dfrac{76}{ - 80}$

$\sf \leadsto y = \dfrac{19}{ - 20}$

$\sf \leadsto y = \dfrac{ - 19}{20}$

Now, by third equation,

$\sf \leadsto x + 2y = \dfrac{ - 3}{4}$

$\sf \leadsto x + 2 \bigg( \dfrac{ - 19}{20} \bigg) = \dfrac{ - 3}{4}$

$\sf \leadsto x + 1 \bigg( \dfrac{ - 19}{10} \bigg) = \dfrac{ - 3}{4}$

$\sf \leadsto x + \dfrac{ - 19}{10} = \dfrac{ - 3}{4}$

$\sf \leadsto \dfrac{10x - 19}{10} = \dfrac{ - 3}{4}$

$\sf \leadsto 4(10x - 19) = 10( - 3)$

$\sf \leadsto 40x - 76 = - 30$

$\sf \leadsto 40x = - 30 + 76$

$\sf \leadsto 40x = 46$

$\sf \leadsto x = \dfrac{46}{40}$

$\sf \leadsto x = \dfrac{23}{20}$

Therefore, the values of x and y are 23/20 and -19/20 respectively.