JEE Main 2026 Apr 2 Shift 2, Mathematics Q3: Linear Equations And Cramer’s Rule

JEE Main2026Apr 2, Shift 2Mathematics

If the system of equations

$x + 5 y + 6 z = 4$ ,

$2 x + 3 y + 4 z = 7$ ,

$x + 6 y + a z = b$

has infinitely many solutions, then the point $(a, b)$ lies on the line

Solution

For infinitely many solutions, the coefficient determinant must vanish.

Setting $D = 156234 16 a = 0$ and expanding gives $a = \frac{50}{7}$ .

Similarly, $D_{z} = 154237 16 b = 0$ yields $b = \frac{29}{7}$ .

Then $a - b = \frac{50 - 29}{7} = 3$ , so the point $(a, b)$ lies on $x - y = 3$ .

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.