Mathematics - Straight Lines Question with Solution | TestHub

Rearrange the given line equation: $(t+1)x+(t-1)y-2t=0$.$tx+x+ty-y-2t=0$.$t(x+y-2)+(x-y)=0$.

For this equation to hold for distinct values of $t$ (implying it's a family of lines passing through a fixed point), the coefficients of $t$ and the constant term must both be zero. Thus,$x+y-2=0$ and $x-y=0$. Solving these two equations gives $x=1$ and $y=1$. So the point of concurrency is $(x_0,y_0)=(1,1)$. Therefore,$x_0+y_0=1+1=2$.