On comparing the ratio, (a1/a2), (b1/b2), (c1/c2) find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 5x – 3y = 11 ; – 10x + 6y = –22
(ii) (4/3)x + 2y = 8 ; 2x + 3y = 12
(i) Given, 5x – 3y = 11 and – 10x + 6y = –22
Therefore,
a1 = 5, b1 = -3, c1 = -11
a2 = -10, b2 = 6, c2 = 22
(a1/a2) = 5/(-10) = -5/10 = -1/2
(b1/b2) = -3/6 = -1/2
(c1/c2) = -11/22 = -1/2
Since (a1/a2) = (b1/b2) = (c1/c2)
These linear equations are coincident lines and have infinite number of possible solutions. Hence, the equations are consistent.
(ii) Given, (4/3)x +2y = 8 and 2x + 3y = 12
a1 = 4/3, b1= 2 , c1 = -8
a2 = 2, b2 = 3 , c2 = -12
(a1/a2) = 4/(3×2)= 4/6 = 2/3
(b1/b2) = 2/3
(c1/c2) = -8/-12 = 2/3
Since (a1/a2) = (b1/b2) = (c1/c2)
These linear equations are coincident lines and have infinite number of possible solutions. Hence, the equations are consistent.