Question

The point of concurrence of the lines $17x+2y-28=0,x+5y+13=0$ and $7x+2y-8=0$ is

• A. $(-2,3)$
• B. $(2,-3)$
• C. $(-2,-3)$
• D. $(2,3)$

Answer 1

The correct option is B $(2,-3)$

Let $(h,k)$ be the point of intersection of the first and second lines.
$17h+2k-28=0h+5k+13=0$
On solving the above equations, we get
$h=2,k=-3$

Substituting $(2,-3)$ in third equation of line, we get
$7\left(2\right)+2(-3)-8=0\Rightarrow 14-14=0$
So, the three straight lines are concurrent.

Hence, the point of concurrence is $(h,k)=(2,-3)$