Answer
See below:
Work Step by Step
Graph each inequality on the same plane.
Step 1: Convert the inequality to an equation by replacing inequality by = sign.
Equation 1: \[x+y\le 6\]
\[x+y=6\]
Equation 2: \[y\ge 2x-3\]
\[y=2x-3\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Equation 1: \[x+y\le 6\]
Make \[x=0\] to find the y-intercept
\[\begin{align}
& x+y=6 \\
& 0+y=6 \\
& y=6
\end{align}\]
Make \[y=0\] to find the x-intercept
\[\begin{align}
& x+y=6 \\
& x+0=6 \\
& x=6
\end{align}\]
The line passes through \[\left( 0,6 \right)\] and\[\left( 6,0 \right)\]. The line is solid since the inequality contains the≤ symbol.
Equation 2: \[y\ge 2x-3\]
Make \[x=0\] to find the y-intercept,
\[\begin{align}
& y=2x-3 \\
& y=0-3 \\
& y=-3
\end{align}\]
Make \[y=0\] to find x-intercept,
\[\begin{align}
& y=2x-3 \\
& 0=2x-3 \\
& x=\frac{3}{2}
\end{align}\]
The line passes through \[\left( 0,-3 \right)\] and\[\left( \frac{3}{2},0 \right)\]. The line is solid since the inequality contains the≥symbol.
Step 3: Choose a test point. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality
Equation 1: \[x+y\le 6\]
\[0\le 6\]
The statement is true. The graph contains the test point.
Equation 2: \[y\ge 2x-3\]
\[0\ge -3\]
The statement is true. The graph contains the test point.
