Assertion (A)
The system of equations $x + y - 8 = 0 and x - y - 2 = 0$ has a unique solutions.
Reason (R)
The system of equations $a_{1} x + b_{1} y + c_{1} = 0 and a_{2} x + b_{2} y + c_{2} = 0$ has a unique solution when $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} .$
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

Option (c) is the correct answer.
Clearly, Reason (R) is false.
On solving x + y = 8 and x − y = 2, we get:
x = 5 and y = 3
Thus, the given system has a unique solution. So, Assertion (A) is true.
∴ Assertion (A) is true and Reason (R) is false.

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