For which value of r does the pair of linear equation have infinitely many solutions:

3x + 2ry - (r + 2) = 0;

rx + y - 1 = 0

- 1, 0
- No solution
- -2, √(3/2)
- ±√(3/2) , 1

Option 2 : No solution

**Given:**

3x + 2ry - (r+2) = 0;

rx + y - 1 = 0

**Calculation:**

From the above equations,

a_{1}/a_{2} = 3/r

b_{1}/b_{2} = 2r/1

c_{1}/c_{2} = (r+2)/1

For infinite solutions,

a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2} ----(i)

From (i),

a1/a2 = b1/b2

⇒ 3/r = 2r/1

⇒ 3 = 2r^{2}

⇒ r = ±√(3/2)

Now,

b1/b2 = c1/c2

⇒ 2r/1 = (r+2)/1

⇒ 2r = r + 2

⇒ 2r - r = 2

⇒ r = 2

After getting the values of r, we find that,

**a1/a2 ≠ b1/b2 ≠ c1/c2**

**So, there are no infinite solutions for the pair of linear equations**

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