Question

4x–19y+13=0, 13x–23y=–19,Solve the given pair of linear equations by elimination method.

Answer 1

Answer :

The given equations are

4x - 19y = - 13 ...(i)

13x - 23y = - 19 ..(ii)

Now, multiplying (i) by 13 and (ii) by 4, we get

52x - 247y = - 169

52x - 92y = - 76

On subtraction, we get

155y = 93

or, y = 3/5

Now, putting y = 3/5 in (i), we get

4x - 19 (3/5) = - 13

or, 4x = - 13 + 57/5

or, 4x = (- 65 + 57)/5

or, 4x = - 8/5

or, x = - 2/5

Therefore, the required solution be

x = - 2/5 and y = 3/5

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Answer 2

Solution :

4x - 19y + 13 = 0

=> 4x - 19y = -13 ---( 1 )

13x - 23y = -19 ---( 2 )

[ 13 × ( 1 ) - 4 × ( 2 ) ] we get,

52x - 247y = - 169

52x - 92y = - 76
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•••••• -155y = -93

=> y = ( -93 )/( -155 )

=> y = 3/5

Put y = 3/5 in equation ( 2 ), we get

13x - 23 × ( 3/5 ) = -19

=> 13x - 23×( 3/5 ) = -19

=> 13x - 69/5 = -19

=> 13x = -19 + 69/5

=> 13x = ( - 95 + 69 )/5

=> x = ( -26 )/( 13 × 5 )

=> x = -2/5

Therefore ,

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

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