Pair of linear equations \(2x+ky=5\) and \(4x+6y=p\) is inconsistent. Which one of the following cannot be the value of \((k+p)\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13
A pair of linear equations \(a_1x+b_1y=c_1\) and \(a_2x+b_2y=c_2\) is inconsistent (has no solution) when the two lines are parallel but not the same:
\(\displaystyle\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\)
Coefficients of \(x\) and \(y\) in the same ratio: \(\displaystyle\frac{2}{4}=\frac{k}{6}\), so \(k=3\)
Constant terms not in that ratio: \(\displaystyle\frac{2}{4}\ne\frac{5}{p}\), so \(p\ne10\)
\(k+p=3+p\), which can be any value except \(3+10=13\)
The other options are possible: 11, 12 and 15 come from \(p=8, 9\) and \(12\).