find the values of a and b for which the simultaneous linear equations x+2y=1 and (a+b)x+(a+b)y=a+b-2 has infinitely many solution
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a = 3 , b = 1 for infinite many solutions of x+2y=1 and (a-b)x+(a+b)y=a+b-2
Step-by-step explanation:
Correction in Question (a+b)x+(a+b)y=a+b-2 should be (a-b)x+(a+b)y=a+b-2
x + 2y = 1
(a-b)x + (a+b)y = a + b - 2
for infinite solution
1/(a - b) = 2/(a + b) = 1/(a + b - 2)
a + b = 2a - 2b
=> a = 3b
2/(a + b) = 1/(a + b - 2)
=> 2a + 2b - 4 = a + b
=> a + b = 4
=> 3b + b = 4
=> 4b = 4
=> b = 1
=> a = 3
(a-b)x+(a+b)y=a+b-2
=> 2x + 4y = 2
=> x + 2y = 1
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