Find whether the following system of equation has a solution or not ? x+5y=10 2x+10y=9

Explanation

Write the given equations in matrix from
`[{:(1,5),(2,10):}][{:(x),(y):}]=[{:(10),(9):}]`
`rArr" "AX=B`
`"Where A=" [{:(1,5),(2,10):}],X=[{:(x),(y):}]" and B="[{:(10),(9):}]`
`therefore" "|A|=|{:(1,5),(2,10):}|=10-10=0`
`therefore" A is not invertible"`.
Co-factores of the elements of matrix A:
`C_(11)=(-1)^(2).10=10`
`C_(12)=(-1)^(3).5=-5`
`C_(21)=(-1)^(3).5=-5`
`C_(22)=(-1)^(4).1=1`
`therefore" adj.A="[{:(C_(11),C_(12)),(C_(21),C_(22)):}]^(1)=[{:(10,-2),(-5,1):}]^(1)=[{:(10,-5),(-2,1):}]`
`"and (adj.A) . B="[{:(10,-2),(-5,1):}][{:(10),(9):}]`
`=[{:(100,-45),(-20,+9):}][{:(55),(-11):}]ne0`
`"Now |A|=0 and (adj.A).B"ne0`
`therefore" Given system of equatino has no solution."`