Question

Find the value of k, for which the system of equations has infinitely many solutions. a) 2x –3y = 7 ; (k+2) x – (2k+1) y = 3(2k–1)

Answer 1

Answer:

K=4

Step-by-step explanation:

Answer 2

The value of k is 2

Step-by-step explanation:

Given system of linear equation:

2x -3y = 7

(k+2)x -(2k+1)y = 3(2k-1)

As system of equations has infinity many solutions if

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

a

2

a

1

=

b

2

b

1

=

c

2

c

1

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

(k+2)

2

=

−(2k+1)

−3

Cross multiply

-(2k+1) \times 2= -3 \times (k+2)−(2k+1)×2=−3×(k+2)

-4k-4= -3k-6−4k−4=−3k−6

simplify the above

-4k+3k= 4-6−4k+3k=4−6

-1k= -2−1k=−2

k= 2k=2