Question

if (k,3) is one solution of equation x-y+1=0,then what is the value of the k?
​

Answer 1

Given that, system of equations x+y−3=0,(1+k)x+(2+k)y−8=0 & x−(1+k)y+(2+k)=0 is consistent.

treating the given system as, 3 equations in 3 variables.

Augumented matrix is

⎣

⎢

⎢

⎡

1

1+k

1

1

2+k

−1−k

0

0

0

3

8

−2−k

⎦

⎥

⎥

⎤

above system is consistent if

∣

∣

∣

∣

∣

∣

∣

∣

1

1+k

1

1

2+k

−1−k

3

8

−2−k

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒(−k

2

+4k+4)+(k62+3k+10)−3(k

2

+3k+3)=0

⇒3k

2

+2k−5=(k−1)(3k+5)=0

∴k=1 or k=

3

−5

Hence, options A and C.

i wish it helps u frnd ✍️✍️✍️