# If the lines 4x+3y=1 ,y=x+5 and 5y+bx=3 are concurrent , then b equals

Solution: If these lines are concurrent , then the intersection point

of the lines $\\ 4x+3y=1 ; and ; y=x+5$ is (-2,3) , which lies on the third line

Hence,

$\\ 5\times 3-2\times b=3\\ \\\Rightarrow 15-2b=3\Rightarrow 2b=12\\ \\\Rightarrow b=6$

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