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Question
Solve th following pair of linear (Simultaneous ) equation using method of elimination by substitution :
`[ 2x + 1]/7 + [5y - 3]/3 = 12`
`[3x + 2 ]/2 - [4y + 3]/9 = 13`
Solution
`[ 2x + 1]/7 + [5y - 3]/3 = 12` (given)
⇒ `[3(2x + 1) + 7(5y - 3)]/21` = 12
⇒ 6x + 3 + 35y - 21 = 252
⇒ 6x + 35y - 18 = 252
⇒ 6x + 35y = 270
⇒ 6x = 270 - 35y
⇒ x = `[270 - 35y ]/6`
`[3x + 2 ]/2 - [4y + 3]/9 = 13` (given)
⇒ `[9(3x + 2) -2(4y + 3)]/18 = 13`
⇒ 27x + 18 - 8y - 6 = 234
⇒ 27x - 8y + 12 = 234
⇒ 27x - 8y = 222 ....(1)
Substituting x = `[ 270 - 35y ]/6` in (1), we get
`27([270 - 35y]/6)` - 8y = 222
⇒ 7290 - 945y - 48y = 1332
⇒ - 993y = - 5958
⇒ y = 6
Substituting y = 6 in x = `[ 270 - 35y ]/6`, we get
x = `[270 - 35 xx 6]/6 = [ 270 - 210]/6 = 60/6 = 10`
∴ Solution is x = 10 and y = 6.
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