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<h4>Cool Down Activity</h4>
<!--Text Entry Interaction Start -->
<p>Solve this system of equations without graphing. Be prepared to show your reasoning.<br>
Use this system of equations to answer questions 1–3.
</p>
<p>\(\left\{\begin{array}{l}5x\;+\;y\;=\;7\\y\;=\;-20x\;+\;2\end{array}\right.\)</p>
<!-- BEGIN TEXT ENTRY WITH REVEAL -->
<br>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4e997994-0aad-4dcf-9325-70170f8ead0c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>What is the \(x\) value?</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> \(\frac15\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!-- END TEXT ENTRY WITH REVEAL -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="c07ed19f-0d53-4979-9b9e-a2e7ad64c830" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="1d10d402-b443-4531-bfcf-dc65abd33808" data-problem-comparator="integer" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>What is the \(y\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 6</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 6.</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>
<!-- END ACTIVITY INPUT 1 TRY -->
<!-- BEGIN TEXT ENTRY WITH REVEAL -->
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="f67c79c6-9e6b-4a1c-ac4e-853809a4aaf9" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Explain your solutions.</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 are some samples.</p>
<ul>
<li>Substituting \( 20x + 2 \) for \( y \) in the first equation, \( 5x+y=7 \), gives \( 5x + (20x+2) = 7 \) or \( 25x + 2 = 7 \), which then gives \( x=\frac15 \). Substituting \( \frac15 \) for \( x \) in the first equation and solving for \( y \) gives \( y=6 \).<br><br></li>
<li>The first equation, \( 5x+y=7 \), can be rearranged to \( y = 7 - 5x \). Substituting \( 7-5x \) for \( y \) in the second equation gives \( 20x + 2 = 7-5x \). Solving this equation leads to \( x=\frac15 \), and substituting \( \frac15 \) for \( x \) in either equation gives \( y=6 \).</li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<!-- END TEXT ENTRY WITH REVEAL -->
<div class="os-raise-student-reflection">
<p class="os-raise-student-reflection-title">Building Character: Growth Mindset</p>
<div class="os-raise-d-flex-nowrap os-raise-gap-1">
<img height="200" src="https://k12.openstax.org/contents/raise/resources/73874f1a255999b5120ed446429bafe1e18ea4c2" width="200px">
<div>
<p class="os-raise-mb-0">Having a growth mindset means believing you can improve your abilities. Compared to a fixed mindset, a growth mindset encourages you to embrace challenges, sustain effort, and try new strategies.</p>
<p>Think about your current sense of having a growth mindset. Are the following statements are true for you?</p>
<ul>
<li>
After I make a mistake, I always look for ways to learn from it.
</li>
<li>
I love challenges because they make me smarter.
</li>
</ul>
<p>Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!</p>
</div>
</div>
</div>