Question

For what value of k will the following pair of linear equations have infinitely many solutions

2x-3y=7
(k+1)x +(1-2k) y = 5k -4

Answer 1

Answer:

$Value \: of \: k = 5$

Step-by-step explanation:

$Given \: pair \: of \: linear \\equations : \\2x-3y -7=0 \:--(1)\\(k+1)x+(1-2k)y-(5k-4)=0\:---(2)$

$Compare \: above\: equations\\with \:a_{1}x+b_{1}y+c_{1}=0,\\a_{2}x+b_{2}y+c_{2}=0$

$a_{1}=2,\: b_{1}=-3,\:c_{1}=-7;\\a_{2}=k+1,\: b_{2}=-1-2k,\:c_{2}=-(5k-4)$

$Now, \\\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\\(Given \: equations \: have \\ infinitly \: many \: solutions )$

$\frac{2}{k+1}=\frac{-3}{1-2k}=\frac{-7}{-(5k-4)}$

$i) \frac{2}{k+1}=\frac{-3}{1-2k}$

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

$\implies 2-4k = -3k-3$

$\implies 2+3= 4k-3k$

$\implies 5=k$

Therefore,

$Value \: of \: k = 5$

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