wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 3
For what values of a and b will the following pair of linear equations have infinitely many solutions?
x + 2y = 1
(a - b)x + (a + b)y = a + b - 2

Open in App
Solution

Given pair of linear equations are
x + 2y = 1
and (a – b) x + (a + b) y = a + b – 2
on comparing with ax + by +c = 0 , we get
a1=1, b1=2 and c1=1a2=(ab), b2=(a+b)and c2=(a+b2)
For infinitely many solutions of the pair of linear equations
a1a2=b1b2=c1c2 1ab=2a+b=1(a+b2)
Taking first two parts
1ab=2a+b a+b=2a2b2aa=2b+ba=3b...(i)
Taking last two parts
2a+b=1(a+b2)2a+2b4=a+ba+b=4...(ii)
Now, put the value of 'a' from Eq (i) in Eq. (ii), we get
3b + b = 4
4b = 4
b = 1
Put the value of b in Eq. (i), we get

a = 3 × 1
a = 3
So, the values (a,b) = (3,1) satisfies the given condition. Hence, required values of a and b are 3 and 1 respectively for which the given pair of linear equations has infinitely many solutions.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon