if the system of following equations in x and y
`2x+3y+4=0,3x+5y+6=0`
`2x^(2)+6xy+5y^(2)+8x+12y+1=t`
Consists of a solution, then find the value of `|t|`

Answer

7

Explanation

Clearly `2x^(2)+6xy+5y^(2)+8x+12y+1=t`
`impliesx(2x+3y+4)+y(3x+5y+6)+4x+6y+1-t=0` ..(i)
The values of x,y that satisfy
`2x+3y+4=0`
`3x+5y+6=0`
Will satisfy the equation (i) if
`4x+6y+1-t=0`
the linear equation will have a solution if they are consistent
i.e., `[{:(2,3,5),(3,5,6),(4,6,1-t):}]=0impliest=-7`