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Solve the following pair of linear equations by the substitution method. (3x)/2 - (5y)/3 = -2, x/y+y/2 = 13/6 - Mathematics

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Solve the following pair of linear equations by the substitution method.

`(3x)/2 - (5y)/3 = -2`

`x/y+y/2 = 13/6`

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Solution

`3/2x - 5/3y = -2 ....(1)`

`x/3+y/2=13/6.....(2)`

From equation (1), we obtain

9x - 10y = -12

`x = (-12+10y)/9 `

Substituting this value in equation  (2), we obtain

`((-12+10y)/9)/3 + y/2 = 13/6`

`(-12+10y)/27+y/2 = 13/6`

`(-24+20y+27y)/54 = 13/6`

47y = 117 + 24

47y = 141

y = 3   (4)

Substituting this value in equation (3), we obtain

x = `(-12+10xx3)/9 = 18/9 = 2`

Hence, x = 2, y = 3

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 1.6 | Page 53
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