Question

$\huge\green{\underline{QUEsTION}}$
FOR which value of a, the pair of equation 9X + aY = 1 and 3X + 4Y = 2 will have a unique solution ?

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Answer 1

Answer:

The given system may be written as

x − 3y − 3 = 0

3x − 9y − 2 = 0

The given system of equation is of the form

a2x + b2y − c2 = 0 a2x + b2y − c2 = 0

Where, a1 = 1, b1 = −3, c1 = −3

a2 = 3, b2 = −9, c2 = −2

We have,

Answer 2

Answer:

Explanation:

In each of the following systems of equation determine whether the system has a unique solution, no solution or infinite solutions. In case there is a unique solution, find it from 1 to 4:

1. x − 3y = 3

3x − 9y = 2

Solution:

The given system of equations is:

x − 3y – 3 = 0

3x − 9y − 2 = 0

The above equations are of the form

a1 x + b1 y − c1 = 0

a2 x + b2 y − c2 = 0

Here, a1 = 1, b1 = −3, c1 = −3

a2 = 3, b2 = −9, c2 = −2

So according to the question, we get

a1 / a2 = 1/3

b1 / b2 = −3/ −9 = 1/3 and,

c1 / c2 = −3/ −2 = 3/2

⇒ a1 / a2 = b1/ b2 ≠ c1 / c2

Hence, we can conclude that the given system of equation has no solution.

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