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<h3>Warm Up Activity<br>
</h3>
<!--Question 1 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="894ee911-0c00-4f53-96be-8b7fb61ad708" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>Andre is trying to solve this system of equations: </p>
<p> \(\left\{\begin{array}{c}x + y &=& 3\\ 4x &=& 12 - 4y\end{array}\right.\)</p>
<p>Looking at the first equation, he thought, “The solution to the system is a pair of numbers that add up to 3. I wonder which two numbers they are.”</p>
<ol class="os-raise-noindent">
<li>Choose any two numbers that add up to 3. Let the first one be the \( x \)-value and the second one be the \( y \)-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: Your answer may vary, but here are some samples.</p>
<p>4 and \(-1\), 0 and 3, \( \frac78 \) and \( 2\frac18 \)</p>
</div>
</div>
<!--Question 2 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="6f8ca407-50d4-43dd-b415-17399d5354ab" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> The pair of values you chose is a solution to the first equation. Check if it is also a solution to the second equation. Then, pause for a brief discussion with your group.</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: Your answer may vary, but here is a sample. </p>
<p>Yes, it is also a solution to the second equation. Sample reasoning for 4 and -1: Substituting 4 and -1 into the second equation gives \(4(4)=12−4(-1)\) or \(16=12+4\), which is a true equation.</p>
</div>
</div>
<!--Question 3 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a2f9a493-db49-414c-8b3b-8a973f5aa34f" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> How many solutions does the system have? Use what you know about equations and solving systems to show that you are right.</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>Infinitely many solutions</p>
</div>
</div>