JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q3

MathematicsSingle correct+4 / -1Question 3 of 90

If the system of equations

$x+y+z=6$
$2x+5y+\alpha z=\beta$
$x+2y+3z=14$

has infinitely many solutions, then α + β is equal to

Answer and worked solution

Official answer: C

Dependence. Row 2 must equal $a(\text{row }1)+b(\text{row }3)$ : $a+b=2$ , $a+2b=5$ give $a=-1$ , $b=3$ .

So $\alpha=-1+9=8$ , $\beta=-6+42=36$ , and $\alpha+\beta=44$ .

(C)

Topics:Systems of linear equations

JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 3