The pair of linear equations 2x+y−3=0 and 6x+3y=9 has ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) a unique solution
(b) two solutions
(c) no solution
(d) infinitely many solutions
Answers
Answered by
9
(d) infinitely many solutions is the correct answer.
Answered by
3
Option ( d ) is correct.
Explanation :
Compare given pair of linear equations
2x + y - 3 = 0 ----( 1 )
6x + 3y - 9 = 0 ---( 2 ) with
a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0 , we get
a1 = 2 , b1 = 1 , c1 = -3 ,
a2 = 6 , b2 = 3 , c2 = -9 ,
Now ,
a1/a2 = 2/6 = 1/3 ,
b1/b2 = 1/3 ,
c1/c2 = ( -3 )/( -9 ) = 1/3
Therefore ,
a1/a2 = b1/b2 = c1/c2 = 1/3
So, the pair of linear equations is not
consistent .
They have infinitely many solutions.
••••••
Explanation :
Compare given pair of linear equations
2x + y - 3 = 0 ----( 1 )
6x + 3y - 9 = 0 ---( 2 ) with
a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0 , we get
a1 = 2 , b1 = 1 , c1 = -3 ,
a2 = 6 , b2 = 3 , c2 = -9 ,
Now ,
a1/a2 = 2/6 = 1/3 ,
b1/b2 = 1/3 ,
c1/c2 = ( -3 )/( -9 ) = 1/3
Therefore ,
a1/a2 = b1/b2 = c1/c2 = 1/3
So, the pair of linear equations is not
consistent .
They have infinitely many solutions.
••••••
Similar questions