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If a 1 , a 2 ,a 3 , a 4 , a 5 , a 6 are in A.P., then prove that the system of equations a 1 x + a 2 y = a 3 , a 4 x + a 5 y = a 6 is consistent

If a1, a2,a3, a4, a5, a6 are in A.P., then prove that the system of equations a1x + a2y = a3, a4x + a5y = a6 is consistent

Grade:12

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
Let a1 = a,  then a2 = a + d, a3 = a + 2d, a4 = a + 3d, a5 = a + 4d, a6 = a + 5d
The equations are consisent if a/a1 # a5 /a2
=> a4 * a2 # a5 * a1
=> (a + 3d) * ( a + d) # (a + 4d) * (a)
=> a2 + 4ad + 3d2 # a2 + 4ad
=> 3d2 # 0  => d # 0
 
Hence the given set of equations are consistent for all the values of except for  d # 0
 
Since a1, a2, a3, a4, a5, aare in AP, assuming that d # 0, the given set of equations are consistent.
 
 
 
 

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