Question

for what values of C the pair of equations 2x+2y=8 and 8x+10y=c have a unique solutions

Answer 1

equations
x-2y-8=0
5x-10y=c



But if c = 40 (real value), then the ratio c1/c2 becomes  1/5 and then the system of linear equations has an infinitely many solutions.
Hence, ate = 40, the system of linear equations does not have a unique solution.

Answer 2

2x +2 y = 8
8 x + 10y = c

a1= 2 , b1 = 2 , c1= 8
a2= 8 , b2= 10 , c2= c

a1/ a2= 2/ 8 =1/4
b1/ b2 = 2/ 10 = 1/5
c1/ c2 = 8/c
thus,
a1/a2 is not equal to b1 / b2.
so, all real values of c, the given pair of the equations have a unique solution.
therefore, the given statement is true.