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

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

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given
(3x/2)-(5y/3) = -2
and
(x/3) + (y/2) = 13/6 are the two equations.
From 1st equation,
we get
(3/2)x = -2 + (5y/3)
⇒ x = 2(-6+5y)/9 = (-12+10y)/9 ………………………(1)
Putting the value of x in the given second equation to get
((-12+10y)/9)/3 + y/2 = 13/6
⇒y/2 = 13/6 –( (-12+10y)/27 ) + y/2 = 13/6
Now, substitute the value of y in equation (1)
we get
(3x/2) – 5(3)/3 = -2
⇒ (3x/2) – 5 = -2
⇒ x = 2
Therefore,
x = 2 and y = 3.
Thanks.

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