Question

find value of a and b for which the system of linear equation has infinite number of solution (a+b)x - 2 b y = 5a+2b+1 3x-y=14

Answer 1

first equation is (a+b)x-2by=5a+2b+13
second equation is 3x-y=14
if two linear equations has infinite solutions,
then, a1/a2=b1/b2=c1/c2
(a+b)/3=-2b/-1=(5a+2b+13)/14
(a+b)/3=2b=(5a+2b+13)/14
to find a,
(a+b)/3=2b
a+b=6b
a=5b
to find b,
2b=(5a+2b+13)/14
(2*14)b=5(5b)+2b+13
28b=25b+2b+13
28b=27b+13
28b-27b=13
b=13
so a=5b
a=5*13
a=65