Question

$\{\begin{array}{c}x+3y\le 18\\ 2x-3y\le 9\end{array}$
If $(a,b)$ is the solution of the above system of linear equation and $a=6$, find the minimum possible value of $b$.

• A. $1$
• B. $-1$
• C. $4$
• D. $-5$

Answer 1

Answer: (A)

$1$

$(6,b)$ is the solution to the given inequalities.

$x+3y\le 18$

$2x-3y\le 9$

When substituted $x=6$, we have

$6+3y\le 18$ or $y\le 4$

The other becomes $12-3y\le 9$ or $y\ge 1$

Thus, the range of $y$ becomes $[1,4]$

Minimum possible $y$ therefore becomes $1$.