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Question
Solve the following pair of linear (simultaneous) equation using method of elimination by substitution:
`[3x]/2 - [5y]/3 + 2 = 0`
`x/3 + y/2 = 2 1/6`
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Solution
`x/3 + y/2 = 2 1/6`
`x/3 + y/2 = 13/6`
⇒ `[2x + 3y]/6 = 13/6`
⇒ 2x + 3y = 13
⇒ 2x = 13 - 3y
⇒ `x = [13 - 3y]/2` ...(1)
And,
`[3x]/2 - [5y]/3 + 2 = 0`
⇒ `3/2([13 - 3y]/2) - [5y]/3 = - 2`
⇒ `[39 - 9y]/4 - [5y]/3 = - 2`
⇒ `[ 117 - 27y - 20y ]/12 = -2`
⇒ `[ 117 - 47y ]/12 = - 2`
⇒ 117 - 47y = - 24
⇒ 47y = 141
⇒ y = 3
Substituting the value of y in (1), we have
x = `[ 13 - 3 xx 3 ]/2`
= `[ 13 - 9 ]/2`
= `4/2`
= 2
∴ Solution is x = 2 and y = 3.
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