Question

for what values 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:

k=5

Step-by-step explanation:

$2x - 3y = 7 - - - - eq1 \\ (k + 1)x + (1 - 2k)y = 5k - 4 - - - - eq2 \\ to \: get \: this \: equation \: as \: infinitely \: many \: solution \: \\ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{2}{k + 1 } = \frac{ - 3}{1 - 2k} = \frac{7}{5k - 4} \\ 2 - 4k = - 3k - 3 \\ - k = - 5 \\ k = 5 \\ - 15k + 12 = 7 - 14k \\ - k = - 5 \\ k = 5$