Question

What value of K will be following pair of linear equations have infinite solutions
2x-3y=7
(K+1)x+(1-2K)y=(5K-4)

Answer 1

Given , 2x-3y = 7 ______ (1)

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

Here $a_1=2,b_1=-3,c_1=7$

$a_2=k+1,b_2=1-2k,c_3=5k-4$

Since equations (1) and (2) have infinite solutions

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_3}$

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

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

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

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

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

$\Rightarrow k=5$