Question

the system of equations 2x-ay =4;5x-ky=5 is inconsistent. if a and k are the natural numbers,then the minimum possible value of (a+k) is equal to​

Answer 1

Answer:

The two equations are inconsistent when a1/a2 =b1/b2

so, now

                       2/5=-a/-k;

                        a =2k/5;

so a+k =2k/5+k =7k/5

now, a and k are natural numbers,  so their sum is also a natural number.

so, for k=5,  a+k =7 (Answer)

Step-by-step explanation:

Answer 2

Answer:

Given

2x-ay =4

5x-ky=5

It is in the form a1x +b1y=c1

and a2x +b2y=c2

here,

a1= 2 , b1 =-a , c1 = 4

a2 = 5 , b2 = -k , c2 =5

since it is a inconsistent solution

so..

a1/ a2 = b1/b2 ≠ c1/c2

2/5 = -a/-k≠ 4/5

2/5=a/k

a=2k/5

the minimum possible value of (a+k) is equal to

a +k

2k/5 + k

=7k /5

a +k =7k /5

a and k are the natural numbers

So a+k is also natural number

For k=1, 2,3,4

a+k is not natural number

For k=5

a+k =7

a+k =7It is a natural number