Question

Find all the positive integer valued solutions $(x,y,z)$ of the systems of inequalities
$\{\begin{array}{ll}3x+2y-z=4,& \\ 2x-y+2z=6,& \\ x+y+x<7.& \end{array}$
Determine how many such triplets exist?

• A. $0$
• B. $1$
• C. $3$
• D. None of these

Answer 1

Answer: (B)

Given equations are
$3x+2y-z=4,\dots (i)$
$2x-y+2z=6\dots (ii)$
$x+y+z<7.\dots (iii)$
By $(i)+2\times (ii),$
$7x+3z=16,$
$\therefore x=1,z=3.$
From $(i),y=2x+2z-6=2$. Since $x=1,$
$y=2,z=3$ satisfy the inequality $(iii)$, the solution is $x=1,y=2,z=3.$