What is the value of (p) for (px+5y=10) and (4x+10y=23) to have no solution?

Correct answer: \(2\)

For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{p}{4}=\frac{5}{10}=\frac{1}{2}\), which gives \(p=2\). Also, \(\frac{10}{23}\ne\frac{1}{2}\), so the two lines are parallel and distinct. Exam tip: first equate the ratios of the coefficients of x and y, then verify that the ratio of the constant terms is different.