Find the value of `aa n db`if thesystem of equation `a^2x-b y=a^2-ba n db x=b^2y=2+4b`(i)posses uniquesolution(ii)infinitesolutions

Find the value of `aa n db`if thesystem of equation `a^2x-b y=a^2-ba n

1.	Find the value of `aa n db`if thesystem of equation `a^2x-b y=a^2-ba n db x=b^2y=2+4b`(i)posses uniquesolution(ii)infinitesolutions
Answer» System of equations is `a^(2)x-by=a^(2)-b" and " bx-b^(2)y =2 +4b` (i) if system has unique solution then lines must be non- parallel or `Delta ne 0` Hence, `\|{:( a^(2),,-b),(b,,-b^(2)):}\| ne0` `" or " -a^(2)b^(2)+b^(2)ne0` ` " or " b^(2) (1-a^(2)) ne0` ` rArr bne " and "ane=1` (ii) if system has infinite solutions then lines must be coincident. Hence `(a^(2))/(b)=(b)/(b^(2)) =(a^(2)-b)/(2+4b)` `rArr b=0 " or " a = ne 1` `" if " a=1 " then " 2 + 4b =b-b^(2)` `" or " b^(2)+3b+2=0` `rArr b=-2 " or " -1` `" if " a=-1 , " then " b=-2 " or " -1` b=0 is not possible Then ordered pairs (a,b) for which system has infintie solutions are `( 1,-2) (1,-1)(-1,-2)(-1,-1)`