The system of equations above has how many solutuions?

2b = 8a

Step-by-step explanation:

The main thing you have to remember before answering the question is

if:

The system has 1 and only solution, then the system will be a1/a2 not equal to b1/b2 = c1/c2

The system has infinitely many solutions then the system will be a1/a2=b1/b2 = c1/c2

The system has no solutions then it will be a1/a2 = b1/b2 not equal to c1/c2

Here, ax + by = 12; 2x + 8y = 60

The system is required to have infinite no. of solutions.

Therefore,

a1/a2=b1/b2=c1/c2

a1/a2 = a/2 (coefficients of x)

b1/b2 = b/8 (coefficients of y)

c1/c2 = - 12/60 = 1/5 (constant terms)

Therefore,

a/2 = b/8 = 1/5

Since a/2 = b/8 then,

2b = 8a

Here, we have to find a/b by transposing.

It is better to take all the variables to one side,

b/a = 8/2 = 4

So a/b will be directly the reverse of it.

Therefore if b/a = 4

Then a/b = 1/4