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Question
Solve the following pair of linear equations by the substitution method.
`(3x)/2 - (5y)/3 = -2`
`x/y+y/2 = 13/6`
Solution
`(3x)/2 - (5y)/3 =-2`
⇒ 9x - 10y = -12 ...(i)
`x/3 + y/2 = 13/6`
⇒ 2x + 3y = 13 ...(ii)
Taking equation (ii)
2x + 3y = 13
⇒ 2x = 13 – 3y
⇒ x = `(13 - 3y)/2`
Now on substituting this value of x in equation (i)
9x – 10y = -12
⇒ `9((13 - 3y)/2) - 10y = -12`
⇒ 117 – 27y – 20y = -24
⇒ 117 – 47y = -24
⇒ 47y = 117 + 24
⇒ 47y = 141
⇒ y = `141/47`
= y = 3
Now on putting y = 3 in equation (i)
⇒ x = `(13 - 3(3))/2`
= `(13 - 9)/2 = 4/2`
= x = 2
Therefore, the solution of the given pair of linear equations is
x = 2 and y = 3
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