Question

x/5-y/3=4/15,x/2-y/9=7/18,Solve the given pair of linear equations by elimination method.

Answer 1

Answer :

Given equations are

x/5 - y/3 = 4/15 ...(i)

x/2 - y/9 = 7/18 ...(ii)

Now, multiplying (i) by (1/2) and (ii) by (1/5), we get

x/10 - y/6 = 2/15

x/10 - y/45 = 7/90

On subtraction, we get

13y/90 = - 1/18

or, y = - 5/13

Now, putting y = - 5/13 in (i), we get

x/5 - (- 5/13)/3 = 4/15

or, x/5 = 4/15 - 5/39

or, x/5 = 9/65

or, x = 9/13

Therefore, the required solution be

x = 9/13 and y = - 5/13

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Answer 2

Solution :

x/5 - y/3 = 4/15

multiply each term by 15 , we get

3x - 5y = 4 -----( 1 )

x/2 - y/9 = 7/18

multiply each term by 18, we get

9x - 2y = 7 ----( 2 )

[ 3 × ( 1 ) - ( 2 ) ] we get,

9x - 15y = 12

9x - 2y = 7
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••••• -13y = 5

=> y = - 5/13

Put y = -5/13 in equation ( 1 ), we get

3x - 5 × ( -5/13 ) = 4

=> 3x + 25/13 = 4

=> 3x = 4 - 25/13

=> 3x = ( 52 - 25 )/13

=> x = ( 27 )/( 13 × 3 )

=> x = 9/13

( x , y ) = ( 9/13 , -5/13 )

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