Answer
The solution set of the system:
\[\left\{ \begin{align}
& x-y<1 \\
& 2x+3y\ge 12 \\
\end{align} \right\}\]
The set of ordered pairs that satisfy \[x-y<1\] and\[2x+3y\ge 12\].
Work Step by Step
Consider the inequality,
\[x-y<1\]
And,
\[2x+3y\ge 12\]
Convert into equality sign, i.e.,
\[x-y=1\] …… (1)
And,
\[2x+3y=12\] ........ (2)
Solve both of the equations individually, then start from equation (1)
\[x-y=1\]
Substitute\[x=0\].
Then,
\[\begin{align}
& -y=1 \\
& y=1
\end{align}\]
And, when substitute\[y=0\].
Then,
\[x=1\]
Then, the line passes through \[\left( 0,-1 \right)\]and\[\left( 1,0 \right)\].
Solve the equation (2),
\[2x+3y=12\]
Substitute\[x=0\].
Then,
\[\begin{align}
& 3y=12 \\
& y=\frac{12}{3} \\
& =4
\end{align}\]
And, when substitute\[y=0\].
Then,
\[\begin{align}
& 2x=12 \\
& x=\frac{12}{2} \\
& =6
\end{align}\]
Then, the line passes through \[\left( 0,4 \right)\]and\[\left( 6,0 \right)\].
