Verified answer

Question:

Find 'c' if the system of the equations cx + 3y + (3 - c) = 0 ; and 12x + cy + c = 0 has infinity many solutions.

SOLUTION:

The two equations are given,

cx + 3y + (3 - c) = 0 ........(i)

12x + cy + c = 0  ............(ii)

Now,

a₁ = c ; b₁ = 3 ; c₁ = (3 - c)

a₂ = 12 ; b₂ = c ; c₂ = ( -c)

For infinity may solution we need,

By putting the values respectively, we get,

Here,

Taking the first two fractions,

By cross multiplication we get,

⇒ 12 * (3) = c * c

⇒ 36 = c²

⇒ √36 = c

⇒ 6 = c

Hence,

The value of 'c' should be (6) for which the two equations will have infinity many solutions.

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Verification,

By putting the value of c,

By simplifying the fraction we get

Hence verified.

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