101646a9-d98e-4918-8ce7-3fdcdcc4a9d2.html

<p dir="ltr"> </p>
<p dir="ltr"><span id="docs-internal-guid-a251ddf1-7fff-4846-ba7e-781e4fda1c22">To help students make connections between systems of equations and systems of inequalities, display the following graphs for all to see.</span></p><span id="docs-internal-guid-a251ddf1-7fff-4846-ba7e-781e4fda1c22"><br>
  <p dir="ltr"><img alt="Graph of 2 intersecting inequalities. Horizontal axis, x, from 0 to 50 by 5s. Vertical axis, y, from 0 to 30 by 5s. Shading right of vertical line and below slanted line. Intersect near 12 comma 13." src="https://k12.openstax.org/contents/raise/resources/f8ace017e1fd7e7fd6a8a83491cac8c4da560835"><br><img alt="Graph of 2 intersecting lines. Horizontal axis, x, from 0 to 50 by 5s. Vertical axis, y, from 0 to 30 by 5s. 1 line is vertical with \(x\)-intercepts of 12. Other line has \(y\)-intercepts of 25." src="https://k12.openstax.org/contents/raise/resources/883cefbfe7f843e5bace8199d5f333472b3df8ea"></p><br>
  <p dir="ltr">Ask students:</p>
  <ul>
    <li aria-level="1" dir="ltr">
      <p dir="ltr" role="presentation">&ldquo;How are the two sets of graphs alike?&rdquo; (They have the same two lines. They can tell us about the solutions to individual equations or inequalities, as well as the solutions to systems.)</p>
    </li>
    <li aria-level="1" dir="ltr">
      <p dir="ltr" role="presentation">&ldquo;How are they different?&rdquo; (The first set of graphs shows two regions that overlap, bounded by dotted lines. The second set shows two intersecting lines, and the lines are solid. One set represents the solutions to a system of linear inequalities.)</p>
    </li>
    <li aria-level="1" dir="ltr">
      <p dir="ltr" role="presentation">&ldquo;How can we tell the number of solutions from each set of graphs?&rdquo; (The graphs representing a system of equations shows one point of intersection, so there is only one solution. The graphs representing a system of inequalities show one region of overlap, but there are many points in that region. This means that there are many solutions.)</p>
    </li>
  </ul>
</span><br><br>