Answer
False
Work Step by Step
Consider the inequality,
\[x-3y<6\]
And,
\[2x+3y\ge -6\]
Convert into equality sign,i.e.,
\[x-3y=6\] …… (1)
And,
\[2x+3y=-6\] ........ (2)
Solve both the equations individually, then start from equation (1)
\[x-3y=6\]
Substitute,\[x=0\].
Then,
\[\begin{align}
& -3y=6 \\
& y=\frac{6}{\left( -3 \right)} \\
& =-2
\end{align}\]
And, when substitute\[y=0\],
Then,
\[x=6\]
Then, the line passes through \[\left( 0,-2 \right)\]and\[\left( 6,0 \right)\].
Solve the equation (2),
\[2x+3y=-6\]
Substitute\[x=0\].
Then,
\[\begin{align}
& 3y=-6 \\
& y=\frac{\left( -6 \right)}{3} \\
& =-2
\end{align}\]
And, when substitute\[y=0\].
Then,
\[\begin{align}
& 2x=-6 \\
& x=\frac{\left( -6 \right)}{2} \\
& =-3
\end{align}\]
Then, the line passes through \[\left( 0,-2 \right)\]and\[\left( -3,0 \right)\].
