JEE Main 2026 Apr 2 Shift 1, Mathematics Q3: Linear Equations And Cramer’s Rule

JEE Main2026Apr 2, Shift 1Mathematics

Let $α, β \in R$ be such that the system of linear equations

$x + 2 y + z = 5$

$2 x + y + α z = 5$

$8 x + 4 y + β z = 18$

has no solution. Then $\frac{β}{α}$ is equal to :

Solution

For no solution, the coefficient determinant must vanish. Expanding along the first row:

$Δ = 121 21 α 84 β = 1 (β - 4 α) - 2 (2 β - 8 α) + 1 (8 - 8) = β - 4 α - 4 β + 16 α = 12 α - 3 β$

Setting $Δ = 0$ gives $β = 4 α$ , hence $β / α = 4$ .

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.