In the equation b = ka + 3, k is a constant. If the possible solutions

\(b=ka+3\)
If \((2, 3)\) is a solution to this,
Then, \(3=2k+3\) or \(2k=0\) or \(k=0\)

Thus, if we are able to determine the value of \(k\) from the options, we can confidently comment on \((2, 3)\) being a solution to the given linear equation or not.

Statement 1:

\((1, 4)\) is a solution to the equation \(b=ka+2\)
Therefore, \(4=k+2\)
Therefore, \(k=2\)

Since, \(k≠0\) we can say that \((2, 3)\) will not be a solution to the given linear equation \(b=ka+3\). Sufficient.

Statement 2:

\((5, 3)\) is a solution to the equation \(3b=ka-1\)
Therefore, \(9=5k-1\)
Therefore, \(5k=10\)
Therefore, \(k=2\)

Since, \(k≠0\) we can say that \((2, 3)\) will not be a solution to the given linear equation \(b=ka+3\). Sufficient.

Hence, either statement alone is sufficient to answer this question, option D.

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Since we are given the equation:

b = ka + 3

And know (a,b) come in this form. In order to determine if (2,3) is a solution we'd need to find out if

b - ka = 3

Hence finding the value of k will allow us to get a yes/no answer, which is sufficient.

==> We can do this if we have the values of a & b and k is the only variable. **No calculations needed!

1) (1, 4) is a solution to the equation b = ka + 2.

We have values of a & b

==> Suff

2) (5, 3) is a solution to the equation 3b = ka - 1.

We have values of a & b

==> Suff

==> D

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