a24a1223-f8bd-4c9d-af48-0b05d4d42c41.html

<h4>Activity (5 minutes)</h4>
<p>This activity gives students a quick exposure to the inequalities \(x&gt;0,\;x\geq0,\;y&gt;0,\;and\;y\geq0,\)&nbsp;so that they are prepared to deal with them later in this lesson. It also reinforces the idea of thinking carefully about whether the points on the boundary lines of a solution region are included in the solution set.</p>
<h4>Student Activity</h4>
<p>Is the ordered pair (5.43, 0) a solution to all, some, or none of these inequalities? Be prepared to explain your reasoning.</p>
<ul>
  <li>\(x &gt; 0\)</li>
  <li>\(y &gt; 0\)</li>
  <li>\(x\;\geq\;0\)</li>
  <li>\(y\;\geq\;0\)</li>
</ul>
<p><strong>Answer:</strong></p>
<p>Some. (5.43, 0) is a solution to \(\;x&gt;0,\;x\geq0,\) and \(y\geq0\). It is not a solution to \(y&gt;0\).</p>
<h4>Activity Synthesis</h4>

<div class="os-raise-usermessage-lightbulb">
  <p>Tip: Remind students that the upper-right region of the coordinate plane is called the first quadrant.</p>
</div>

<p>Invite students to share their responses. Then, display a blank four-quadrant coordinate plane for all to see.&nbsp;</p>
<p>&nbsp;<img alt="Blank x y coordinate plane.
&nbsp;" src="https://k12.openstax.org/contents/raise/resources/44e5c41f2c2ceb7faca155b36b03bf44511d3969"></p>
<p><strong>Use the following questions to lead a class discussion. </strong></p>
<ul>
  <li>"If we were to graph the solutions to \(x&gt;0\), what would the region look like?" (We would shade the right side of the \(y\)-axis.) "Is the \(y\)-axis included in the solution region?" (No)</li>
  <li>"What about the graph of the solutions to \(y&gt;0\)?" (We would shade the upper side of the \(x\)-axis). "Is the \(x\)-axis included in the solution region?" (No)</li>
  <li>"What about the graph of the solutions to the system \(x&gt;0\) and \(y&gt;0\)?" (The solution region would be the upper-right section of the graph, where the other two regions overlap.)</li>
</ul>