Question

For what values of ‘k’ will the following pair of linear equations will have infinetly
many solutions?
2x + 3y = k ; (k – 1)x + (2k – 1)y = 4k + 1

Answer 1

Answer:

Step-by-step explanation:

If a pair of linear equations is inconsistent, then their graph lines will be. ... If a pair of linear equations in two variables is inconsistent, then no solution exists as they have no common point. And, since there is no common solution, their graph lines do not intersect. Hence, they are parallel

Answer 2

Step-by-step explanation:

Solution :

We have,

2x + 3y = 7

=> 2x + 3y - 7 = 0

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

=> (k + 1)x (2k - 1)y - (4k + 1) = 0

For infinitely,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

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

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

$= > 2(2k + 1) = 3(k + 1)$

$= > 4k - 2 = 3k + 3$

$= > 4k - 3k = 3 + 2$

$= > k = 5$

Hence :

The value of k is 5.