Question

If the system of cquations 7x-y- 5=0 and ax-5y-25=0 has infinite number of solutions, then for k∈IR the general Solution (x,y) of the system is

Answer 1

since 7x-y-5=0 and ax-5y-25=0 has infinite sol.

a1/a2=b1/b2=c1/c2

7/a=-1/-5=-5/-25

7/a=-1/-5. 7/a=-5/-25

7/a=1/5. 7/a=5/25

a=35. 5a=175

a=175/5=35

since a=35

Answer 2

if both have infinite soln then both en will coincide

so 7/a = -1/-5= -5/-25

a=35

now let x=k

then on putting it in eqn 1 we get y=7k-5

so gen sol is (k, 7k-5)

(k, 7k-a/7)