Question

For what values of a and b do the equation 2x - y = 4b and ax/3 + by = -4b have more than one solution. Plz help me

Answer 1

for more than 1 solution these line should concide each other's....
so
2x-y= 4b.......
ax/3+ by= -4b
2/(a/3)= -1/b= 4b/(-4b)
so
2/(a/3)= 4b/(-4b)
2/(a/3)= -1
-a/3= 2
a= -6.......
again -1/b= 4b/(-4b)
-1/b= -1
b = 1....

Answer 2

2x-y=4b. ax/3+by=-4b
a1=2, b1=-1, c1=4b, a2=a/3, b2=b, c2=-4b
For the pair of equations to not have one solution, they have to coincide with each other,
a1/a2=b1/b2=c1/c2
So,
2/(a/3)=-1/b=4b/-4b
6/a=-1/b=1/-1
6/a=-1/b=-1
Then,
6/a=-1/b
6b=-a [1]
And,
-1/b=-1
-1(-1)=b
1=b [2]
Substituting eqn. 2 in eqn. 1
6(1)=-a
6=-a
a=-6

So, for pair if equations to have more than one solution, a is -6 and b is 1.

Hope this helps you!!