State whether the given statement is true or false.The pair of equations x+3y=6   and x−3y=12   are consistent with unique solutions.

# State whether the given statement is true or false.The pair of equations   and   are consistent with unique solutions.

1. A
True
2. B
False

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### Solution:

Given that the following pairs of linear equations   and   are consistent with unique solution. We need to find whether the given statement is true or false.
A system of linear equations   and   is consistent with unique solution when  .
From equations   and  , we have,
and
Now, we have,
And,

Hence, we can observe that,

Thus, the given pair of equation are consistent with unique solutions.
Therefore, the given statement in the question is true.
Therefore, option 1 is the correct choice.

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