find the HCF of roots of linear equation system x+2y=12,2x-3y=3
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Given:
Linear equation system x+2y=12, 2x-3y=3
To Find:
HCF of roots of linear equation system.
Solution:
Solving x+2y=12, 2x-3y=3
- x + 2y = 12 - ( 1 )
- 2x - 3y = 3 - ( 2 )
Solving for y,
- 2 x ( 1 ) - ( 3 ) = > (2x + 4y = 24 ) - ( 2x - 3y = 3 )
- 7y = 21
- y = 3.
Solving for x ,
- x = 12 - 6 = 6 .
Now we have to find the Highest Common Factor of 6 and 3 .
- Factors of 3 : 1, 3.
- Factors of 6: 1 , 2, 3, 6.
Therefore, HCF( 3, 6 ) = 3
The HCF of roots of linear equation system x+2y = 12, 2x-3y=3 is 3.
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