Question

plz can anyone solve this step by step and send the answer plz its urgent​

Answer 1

Answer:

a = 3 and b = 1.

Step-by-step explanation:

Given equations are:

x + 2y = 1

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

We know that for a system of linear equations to have infinitely many solutions, the coefficients of the unknown variables (x and y) and the constant terms must be in proportion

So, for the given system, we must have

a₁/a₂ = b₁/b₂=c₁/c₂

For x+2y - 1= 0 => a₁ = 1, b₁=2, c₁ = -2

For (a-b)x+(a+b)y - (a+b-2) = 0 => a₂ = a-b, b₂ = a+b, c₂ = - (a+b-2)

1/a-b = 2/a+b = -1/-(a+b-2) (∵a₁/a₂ = b₁/b₂=c₁/c₂)

Now we have from above that

1/a-b = 2/a+b

=> a+b = 2(a-b)

=> 2a - a = 3b

=> a = 3b

and

2/a+b = 1/(a+b-2)

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

2a+2b - 4 = a + b

a+b = 4

3b +b = 4  (∵a = 3b)

4b = 4

=> b = 1

=> a = 3b = 3*1 = 3.

Thus the values are a = 3 and b = 1.

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