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  • For the pair of equations lambdax + 3y = –7 2x + 6y = 14 to have infinitely many solutions, the value of lambda should be 1. Is the statement trueGive reasons.

For the pair of equations \lambdax + 3y = –7 ,2x + 6y = 14to have infinitely many solutions, the value of \lambda should be 1. Is the statement true?Give reasons.

Answers (1)

Solution:
Here equations are \lambda x + 3y = –7
2x + 6y = 14
a1 = \lambda , b1 = 3, c1 = 7
a2 = 2, b2 = 6, c2 = –14
The equation have infinitely many solution

\therefore \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}
\frac{\lambda }{2}= \frac{3}{6}\neq \frac{-7}{14}
Here we can see that

\frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}
Hence no value of \lambda exist because it is given that equation has infinitely many solutions
Hence the statement is false.

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infoexpert27

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