For (6x+12y=30) and (kx+2y=8) to have no solution, what is the value of (k)?

Correct answer: \(k=1\)

For no solution, the two lines must be parallel but distinct. Thus, the ratios of the coefficients of x and y must be equal, while the ratio of the constants must be different. Here, \(\frac{12}{2}=6\), so \(\frac{6}{k}=6\) gives \(k=1\). The equations then become \(x+2y=5\) and \(x+2y=8\), which represent distinct parallel lines. For \(k=2\) or other listed values, the coefficient ratios are not equal. Exam tip: first equate the coefficient ratios, then check that the constant ratio differs.