Question

If the system of simultaneous linear equations \(x - 2y + z = 0\), \(2x + 3y + z = 6\) and \(x + 2y + pz = q\) has infinitely many solutions, then

• A. \(p + q = 4\)
• B. \(pq = \frac{48}{49}\)
• C. \(q - p = 3\)
• D. \(\frac{p}{q} = 4\)

Hint:

When establishing infinite solutions, always solve for the principal determinant \(D = 0\) first to find one parameter, then pick the easiest \(D_x, D_y,\) or \(D_z\) containing the second parameter.

Answer 1

The Correct Option is C