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For the pair of equations
$ \lambda x+3 y=-7 $
$ 2 x+6 y=14 $
to have infinitely many solutions, the value of $ \lambda $ should be 1 . Is the statement true? Give reasons.
The given pair of equations is,
\( \lambda x+3 y=-7 \)
\( 2 x+6 y=14 \)
To find :
We have to find whether the value of \( \lambda \) is 1.
We know that,
The condition for infinitely many solutions is,
\( \lambda x+3 y+7=0 \)
\( 2 x+6 y-14=0 \)
$a_1=\lambda, b_1=3, c_1=7$
$a_2=2, b_2=6, c_2=-14$
$\lambda$ does not have a unique value.
Hence, for no value of $\lambda$ the given pair of linear equations has infinitely many solutions.
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