If the system of equations \[ \begin{aligned} & x+5 y+6 z=4 \\ & 2 x+3 y+4 z=7 \\ & x+6 y+a z=b \end{aligned} \] has infinitely many solutions, then the point $(\mathrm{a}, \mathrm{b})$ lies on the line

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Matrices

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

Answer: (B)

For infinitely many solutions the third equation must be a combination

p (Eq_{1}) + q (Eq_{2})

. Matching the

x

- and

y

-coefficients,

p + 2 q = 1

and

5 p + 3 q = 6

, giving

p = \frac{9}{7}, q = - \frac{1}{7}

. The

z

-coefficient and constant then give

a = 6 p + 4 q = \frac{50}{7}

and

b = 4 p + 7 q = \frac{29}{7}

. Hence

a - b = \frac{50 - 29}{7} = 3

, so

(a, b)

lies on

x - y = 3

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option