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# Solve the Following Simultaneous Equations. 2 X + 3 Y = 13 ; 5 X − 4 Y = − 2 - Algebra

Sum

Solve the following simultaneous equations.
2/x + 3/y = 13 ; 5/x - 4/y = -2

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#### Solution

2/x + 3/y = 13 ; 5/x - 4/y = -2
Let 1/x = u and 1/y = v
So, the equations obtained are
2u + 3v = 13                        ........(I)       ( x 5)
5u - 4v = -2                         .........(II)      ( x 2)
10u + 15v = 65                   ..........(III)
10u - 8v = - 4                     ...........(IV)
Subtracting (IV) from (III)
23v = 69
⇒ v = 3
Putting the value of v in (I)
2u + 3 x 3 = 13
⇒ 2u = 4
⇒ u =2
1/x = u ⇒ x = 1/u = 1/2
1/y = v  ⇒ y = 1/v = 1/3

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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 5 Linear Equations in Two Variables
Problem Set 5 | Q 4.3 | Page 91
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