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f6adfaf1-d357-45d5-8c0d-5eab5beed536.html
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<h4>Cool Down Activity</h4>
<p>Graphing technology should not be used in this cool down.<br>
</p>
<h4>Student Activity</h4>
<p>Use this linear equation to answer questions 1 - 2.</p>
<p> \(\left\{\begin{array}{c}2x+\frac12y=7\\6x- \frac12y=5\end{array}\right.\)</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="6a4f62a6-3514-4990-80d3-bb9ece07a4b5" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#1.-->
<div class="os-raise-ib-pset-problem" data-content-id="6b5fdee3-467c-42a4-b98d-d5e30434c8e9" data-problem-type="dropdown" data-solution="Adding the two equations" data-solution-options='["Adding the two equations", "Subtracting one from the other"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li> Which would be a more helpful method for solving the system? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is to add the two equations.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is to add the two equations.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="901a641e-26d8-4a24-9d1c-3c7dd68403b7" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> Explain or show how you know. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample. \(\frac12y + − \frac12y = 0\), so adding the equations would eliminate the \(y\)-variable and enable solving for \(x\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>Solve the system without graphing to answer questions 3–5.</p>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="79417417-f19d-4570-bb90-e3a421d9c46d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> Identify the \(x\) coordinate of the solution. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(\frac32\) or equivalent</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="524fa8b7-f470-40b2-af10-f2916c596ede" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#4-->
<div class="os-raise-ib-pset-problem" data-content-id="ed1b5c81-1750-469d-8d13-0383aa66fb24" data-problem-comparator="integer" data-problem-type="input" data-solution="8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li> Identify the \(y\) coordinate of the solution. </li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is 8. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is 8.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Q#5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="775a1d95-b6dc-4b3a-97f7-a39d0a18f6fb" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li> Explain or show your reasoning. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<p> \(\begin{array}{r}\underline{\;\;\;\;\;\;\;\;\;\;2x+\frac12y=7\\+\;\;\;\;\;\;6x-\frac12y=5}\\8x=12\\x=\frac{12}8\\x=\frac32\\\end{array}\) </p>
</div>
</div>
<!--Interaction End -->
<br>
<h4>Video: Determining the Best Method for Solving a System of Equations</h4>
<p> Watch the following video to learn more about finding the best method to solve a system of equations.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/e4e00f7b211b8de51eafad8be8fa2e15f9c49e04">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/af1c3c241d3175f31358f10ec23544a1f4ab1758" srclang="en_us">
https://k12.openstax.org/contents/raise/resources/e4e00f7b211b8de51eafad8be8fa2e15f9c49e04
</video></div>
</div>