Question

For what value of k the following pair of linear equation has infinite number of solutions :2x+(k-2)y=k: 6x+(2k-1)y=(2k+5).
Please solve it fast it’s urgent

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$Value \: of \: k = 5$

Step-by-step explanation:

Given system of linear equations:

2x+(k-2)y-k=0 ---(1)

6x+(2k-1)y-(2k+5)=0---(2)

$Compare\: these\: equations\: with \:\\</p><p>a_{1}x+b_{1}y+c_{1}=0\: and \\</p><p>a_{2}x+b_{2}y+c_{2}=0,we\:get$

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\\given \: linear \: equations \: has \\\: infinite \: number \: of \: solutions$

$\implies \frac{2}{6}=\frac{k-2}{2k-1}$

$\implies \frac{1}{3}=\frac{k-2}{2k-1}$

$\implies 2k-1=3(k-2)$

$\implies 2k-1=3k-6$

$\implies -1+6=3k-2k$

$\implies 5=k$

Therefore,

$Value \: of \: k = 5$

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