Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • For which values of a and b, will the following pair of linear equations have infinitely many solutionsx + 2y = 1 (a – b)x+ (a + b)y = a + b – 2

For which 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

Answers (1)

Solution:
The given equations are
x + 2y = 1
(a – b) x + (a + b)y = a + b – 2
In equation
x + 2y = 1
a1 = 1, b1 = 2, c1 = –1
In equation
(a – b)x (a + b)y = a + b – 2
a2 = (a – b), b2 = (a + b), c2 = – (a + b – 2)
\frac{a_{1}}{a_{2}}= \frac{1}{\left ( a-b \right )},\frac{b_{1}}{b_{2}}= \frac{2}{\left ( a+b \right )},\frac{c_{1}}{c_{2}}= \frac{-1}{-\left ( a+b-2 \right )}

For infinitely many solutions  \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}
 

\frac{1}{\left ( a-b \right )}= \frac{2}{\left ( a+b \right )}= \frac{1}{a+b-2 }

\frac{1}{\left ( a-b \right )}= \frac{2}{\left ( a+b \right )}\; \;

a + b = 2a –2b

–a + 3b = 0 … (1)

\frac{2}{\left ( a+b \right )}= \frac{1}{a+b-2}

2a + 2b – 4 = a + b

a + b –4 =  0 …(2)

Add equations (1) and (2)
–a + 3b + a + b = 0 + 4
4b = 4
b = 1
Put b = 1 in equation (1)
–a + 3 (1) = 0
a = 3
Hence a = 3 and b = 1.

Posted by

infoexpert27

View full answer

Similar Questions

Latest Question