linear equation 2x+3y+13=0,8x-4y+4=0
Answers
Answer:
oncept:
\textsf{If the lines ax+by+c=0, lx+my+n=0, px+qy+r=0 are concurrent, then}If the lines ax+by+c=0, lx+my+n=0, px+qy+r=0 are concurrent, then
\begin{gathered}\bf\left|\begin{array}{ccc}a&b&c\\l&m&n\\p&q&r\end{array}\right|=0\end{gathered}
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a
l
p
b
m
q
c
n
r
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=0
\textsf{Since the lines 3x-4y-13=0, 8x-11y-33=0, 2x-3y+k=0 are concurrent,}Since the lines 3x-4y-13=0, 8x-11y-33=0, 2x-3y+k=0 are concurrent,
\begin{gathered}\bf\left|\begin{array}{ccc}3&-4&-13\\8&-11&-33\\2&-3&k\end{array}\right|=0\end{gathered}
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3
8
2
−4
−11
−3
−13
−33
k
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=0
\implies\,3(-11k-99)+4(8k+66)-13(-24+22)=0⟹3(−11k−99)+4(8k+66)−13(−24+22)=0
\implies\,-33k-297+32k+264+26=0⟹−33k−297+32k+264+26=0
\implies\,-k-7=0⟹−k−7=0
\implies\,k+7=0⟹k+7=0
\implies\boxed{\bf\,k=-7}⟹
k=−7
\therefore\textsf{The value of k is -7}∴The value of k is -7