Question

Find the value of k, if the pair of equations 2x + 5y=k and
10x + 25y=15 have no solution.​

Answer 1

$Compare \: given \: system \:of \: linear \\equations : 2x + 5y - k = 0 \:and \\10x +25y - 15 = 0 \: with \\a_{1}x + b_{1}y + c_{1} = 0 \: and \\a_{2}x + b_{2}y + c_{2} = 0 , we \:get$

$a_{1} = 2, b_{1} = 5 , c_{1} = -k \\a_{2} = 10, b_{2} = 25 , c_{2} = -15$

$\boxed { \pink { \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} ≠\frac{c_{1}}{c_{2}} }}$

$\blue { ( Given \: equations \:have \:no \: solution )}$

$\implies \frac{b_{1}}{b_{2}} ≠\frac{c_{1}}{c_{2}}$

$\implies \frac{5}{25}≠ \frac{-k}{-15}$

$\implies \frac{5}{25}≠ \frac{k}{15}$

$\implies \frac{5}{25}\times 15 ≠ k$

$\implies 3 ≠ k$

Therefore.,

$\red { k } \green {≠3}$

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