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cc98afef-8ec5-45b7-a3f2-955512400b3c.html
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<h3>Activity <br>
</h3>
<p>Make sense of Diego’s work and discuss with a partner, then answer questions 1 - 3.</p>
<p>\(\left\{\begin{array}{l}2x\;-\;3y\;=\;-4\\2x\;+\;3y\;=\;8\end{array}\right.\)</p>
<p>
\(4x = 4\\
x = 1\\
2(1) + 3y = 8\\
3y = 6\\
y = 2
\)
</p>
<br>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="32b9325f-7340-4d27-86ad-f4c28122c73a" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> What did Diego do to solve the system? </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. Diego added the two equations, and the sum is an equation with only one variable, \(x\), which can be solved. He then substituted the \(x\)-value into the second equation and solved for \(y\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="bc62eabc-71ca-4e9b-96dd-790cfdbfdb14" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"> <!--Q#2.-->
<div class="os-raise-ib-pset-problem" data-content-id="332656da-9c94-4a72-80e4-fc18b7d3367c" data-problem-type="dropdown" data-solution="Yes" data-solution-options='["Yes", "No"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li> Is the pair of \(x\)- and \(y\)-values that Diego found actually a solution to the system? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is yes.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Try again. The answer is yes.</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#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5bfddc6e-0f9d-4031-8949-91020b0c6bfd" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> How do 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> When the values are substituted back to the equations in the system, they make the equations true.</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>For questions 4–7 determine if Diego’s method will work for solving the system. Be prepared to show your reasoning. If Diego’s method does not work, use a different method to solve and get the answers.</p>
<p>\(\left\{\begin{array}{l}\begin{array}{rcl}2x+y&=&4\\x-y&=&11\end{array}\end{array}\right.\)</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="b6b18f31-18f1-42e8-8b19-49bc98ab155c" 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="a1c65390-c43c-4b57-8f14-96cd29348568" data-problem-type="dropdown" data-solution="Yes" data-solution-options='["Yes", "No"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li> Will Diego’s method work for solving the system? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is yes.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is yes.</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>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="222ddb1c-f07e-457f-9782-b46be76636cd" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="fe7c7f26-3863-4651-9e81-6e44d1190d77" data-problem-comparator="integer" data-problem-type="input" data-solution="5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li> What is the \(x\) value? </li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is 5.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is 5.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q#6-->
<div class="os-raise-ib-pset-problem" data-content-id="b4a6ed6d-091f-482c-ba30-81085479bb05" data-problem-comparator="float" data-problem-type="input" data-solution="-6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<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! The answer is -6.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The 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>
<br>
<!--Q#7-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ed123ccd-87ce-4364-accd-8b88e58d4b36" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="7">
<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 is a sample. Adding the two equations gives \(3x=15\), or \(x=5\). Substituting 5 for \(x\) in either one of the original equations gives \(y=−6\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>For questions 8–11 determine if Diego’s method will work for solving the system. Be prepared to show your reasoning. If Diego’s method does not work, use a different method to solve and get the answers.</p>
<p>\(\left\{\begin{array}{lc}\begin{array}{rcl}8x+11y&=&37\;\;\\8x+y&=&7\end{array}\end{array}\right.\)</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="9e5adac7-a890-4399-bfdc-5c8c2e3d5d8f" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#8.-->
<div class="os-raise-ib-pset-problem" data-content-id="77cd723b-2ccc-4320-aa59-ec709732e366" data-problem-type="dropdown" data-solution="No" data-solution-options='["Yes", "No"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li> Will Diego’s method work for solving the system? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The answer is no.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is no.</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#9-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a11e9098-0ac3-48dd-807f-3b0446c3860b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="9">
<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></p>
<p> \(\frac12\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="d85ba6ef-d816-47ee-b23d-98e11a09273b" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#-->
<div class="os-raise-ib-pset-problem" data-content-id="20909679-742b-4d6b-a5eb-04c5fdd04a82" data-problem-comparator="integer" data-problem-type="input" data-solution="3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<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! The answer is 3. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The answer is 3.</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#11-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="723bed98-ce73-4c47-b14c-0ed140ce06da" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="11">
<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 is a sample. Diego’s method does not work because adding the two equations doesn’t get us anywhere. The sum is \(16x+12y=44\), which doesn’t make it easier to solve.</p>
<p>It works if the second equation is subtracted from the first instead of added to the first. The difference is \(10y=30\), or \(y=3\). If we substitute 3 for \(y\) in one of the original equations, we get \(x=\frac12\).</p>
</div>
</div>
<!--Interaction End -->