JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q4

MathematicsSingle correct+4 / -1Question 4 of 90

The ordered pair $(a,b)$ , for which the system of linear equations
$3x-2y+z=b$
$5x-8y+9z=3$
$2x+y+az=-1$
has no solution, is :

\left(3,\dfrac13\right)

\left(-3,\dfrac13\right)

\left(-3,-\dfrac13\right)

\left(3,-\dfrac13\right)

Answer and worked solution

Official answer: C

Determinant. $3(-8a-9)+2(5a-18)+(5+16)=-14a-42=0$ , so $a=-3$ .

Dependence. With $a=-3$ , row 2 $=3\times$ row 1 $-2\times$ row 3 on the left side, so consistency needs $3b-2(-1)=3$ , i.e. $b=\frac13$ .

No solution for $a=-3$ , $b\ne\frac13$ : of the options, $\left(-3,-\frac13\right)$ .

(C)

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 4