Math, asked by dheerajlife, 1 year ago

for which values of a and b does the following pair of linear equation have infinitely many solution 2x+y=7 (a-b)x + (a+b)y= 3a+b-2

Answers

Answered by kishanswaroopya
2
GIVEN
pair of linear equation have infinitely many solution
2x+y=7 .............. (1)
(a-b)x + (a+b)y= 3a+b-2 ............ (2)

FORMULA for infinite many solutions
a1 / a2 = b1 / b2 = c1 / c2

Therefore,
2 / (a - b) = 1 / (a + b) = 7 / 3a + b + 2
Take
2 / (a - b) = 1 / (a + b)
2a + 2b = a - b
2a - a = - b - 2b
a = - 3b - - - - - - - - - - - - - - - - (1)
Now take
1 / (a + b) = 7 / 3a + b + 2
3a + b + 2 = 7a + 7b
3a + b + 2 - 7a - 7b = 0
- 4a - 4b + 2 = 0
4a + 4b = 2
2a + 2b = 1 - - - - - - - - - - - - - - (2)

SUBSITUTE (1) value in (2)
2(-3b) + 2b = 1
- 6b + 2b = 1
-4b = 1
b = - 1 / 4
Subsitute b value in (1)
a = - 3 (- 1 / 4)
a = 3 / 4

Therefore, a = 3 / 4 and B = - 1 / 4

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