Question

for what value if k the following pair of linear equations has infinite number of solutions
x + (2k-1)y = 4
kx+ 6y = k + 6​

Answer 1

Answer:

Here is your answer :-

In these equations ,

a = k , b = 3 , c = (2k+1)

A = 2(k+1) , B = 9 , C = (7k+1)

These equations has infinity solutions . so ,

a/A = b/B = c/C

k/2k+2 = 3/9 = 2k+1/7k+1

(1) k/2k+2 =3/9

9k = 6k +6

3k = 6

k = 2

So , the value of k is 2

Hope it helps you ..thanks

Step-by-step explanation:

Answer 2

Answer:

If a set of equations has an infinite number of solutions, then:

$\frac{a_{1} }{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Thus,

$\frac{x}{k}=\frac{2k-1}{6}=\frac{-4}{-k-6}$

$\frac{2k-1}{6}=\frac{-4}{-k-6}$

$(2k-1)(-k-6)=6(-4)=-24\\-2k^{2} - 12k+k+6=-24\\ -2k^{2}-11k+6=-24\\-2k^{2}-11k+30=0\\2k^{2}+11k-30=0\\2k^{2}+4k-15k-30=0\\2k(k+2)-15(k+2)=0\\(2k-15)(k+2)=0$

Hence:

$k=\frac{15}{2}$ or $k=-2$