Question

6. 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
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Answer 1

✓✓✓✓ANSWER

X+2y=1

=>X+2y-1=0......(I)

(a - b)x + (a+b)y= a + b - 2

=>(a - b)x + (a+b)y-( a + b - 2)=0.....(I)

the equations will have infinitely many solutions if

$\frac{1}{(a - b)} = \frac{2}{(a + b)} = \frac{1}{a + b - 2} \\ \\ or \\ \frac{1}{(a - b)} = \frac{2}{(a + b)} \\ = > a + b = 2a - 2b \\ 3b = a$

$a + b - 2 = a - b \\ 2b = 2 \\ b = 1 \\ therefore \: \: \: a = 3$