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

Varna Venugopal

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

Jul 30, 2017 •Comment

Chris Lele, Magoosh Tutor

Apr 13, 2016 •Comment