Question

5ax+6by=28; 3ax+4by=18,Solve the given pair of linear equations by elimination method.

Answer 1

Answer :

Given equations are

5ax + 6by = 28 ...(i)

3ax + 4by = 18 ...(ii)

Now, multiplying (i) by 3 and (ii) by 5, we get

15ax + 18by = 84

15ax + 20by = 90

On subtraction, we get

2by = 6

or, y = 3/b

Now, putting y = 3/b in (i), we get

5ax + 6b (3/b) = 28

or, 5ax + 18 = 28

or, 5ax = 28 - 18

or, 5ax = 10

or, x = 2/a

Therefore, the required solution be

x = 2/a and y = 3/b

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Answer 2

Solution :

5ax + 6by = 28 ---( 1 )

3ax + 4by = 18 --- ( 2 )

[ 3 × ( 1 ) - 5 × ( 2 ) ] we get

15ax + 18by = 84 --- ( 3 )

15ax + 20by = 90---( 4 )
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•••••••• - 2by = - 6

=> y = ( -6 )/( -2b )

=> y = 3/b

Put y = 3/b in equation ( 1 ), we get

5ax + 6b ( 3/b ) = 28

=> 5ax + 18 = 28

=>5ax = 10

=> x = 10/5a

=> x = 2/a

Therefore ,

( x , y ) = ( 2/a , 3/b)

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