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<h4>Activity</h4>
<p>Solve each system without graphing.</p>
<br>
<p>Use this system of equations to answer questions 1–3.</p>
<blockquote>
<p>\( \begin{cases} x + 2y = 8 \\x = -5 \end{cases} \)</p>
</blockquote>
<p>Here are the four systems of equations you saw in the previous exercise. Solve each system. Then, check your solutions by substituting them into the original equations to see if the equations are true.
</p>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="435da4fe-abe1-4a68-b93e-55de01a4ad8e" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="33fba438-5fcc-4669-afb7-7f659afd783b" 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 \(x\) 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 -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="4a9c0a5d-3233-4cc6-bc3b-097009a3c078" 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="b552fe1d-7d76-4a1e-b0a4-b65888a5a287" data-problem-comparator="integer" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<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! 2</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 2.</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 CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q3-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="3">
<li>Explain your solution.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
5x-2y&=&26
\\ 5(y+4)-2y&=&26
\\ 5y+20-2y&=&26
\\ 3y+20&=&26
\\ 3y&=&6
\\ y&=&=2
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
\\ 2+4&=&x
\\ 6&=&x
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN SIDE BY SIDE EQUATIONSS-->
<p>\(\begin{array}{rcr}
5(6)-2(2)=26 & & \\
30-4\overset?=26 & & 2+4\overset?=6 \\
26=26\checkmark & & 6=6\checkmark
\end{array}\) </p>
<!--END SIDE BY SIDE EQUATIONS -->
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<br>
<p>Use this system of equations to answer questions 4-6.</p>
<blockquote>
<p>\( \begin{cases} 2m - 2p = -6\\ p = 2m + 10 \end{cases} \)</p>
</blockquote>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="c1663edd-a3e8-4e7c-a4d6-31cd3b333672" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="c58b42e1-2db3-413d-9503-72c0745a55a7" data-problem-comparator="integer" data-problem-type="input" data-solution="-7">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>What is the \(m\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -7</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is -7.</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 -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="09ecf2e6-bf0d-432c-8527-05db0a08a238" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="6f943379-eb55-44a5-9c30-69d7b46fa41d" data-problem-comparator="integer" data-problem-type="input" data-solution="-4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>What is the \(p\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -4</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is -4.</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 CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q6-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="6">
<li>Explain your solution.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal2">
<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
2m-2p&=&-6
\\ 2m-2(2m+10)&=&-6
\\ 2m-4m-20&=&-6
\\ -2m-20&=&-6
\\ -2m&=&14
\\ m&=&-7
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
p&=&2m+10
\\ p&=&2(-7)+10
\\ p&=&-14+10
\\ p&=&-4
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN SIDE BY SIDE EQUATIONSS-->
<p>\(\begin{array}{rcr}
2(-7)-2(-4)=-6 & & -4=2(-7)+10\\
-14+8\overset?=-6 & & -4\overset?=(-14)+10 \\
-6=-6\checkmark & & -4=-4\checkmark
\end{array}\) </p>
<!--END SIDE BY SIDE EQUATIONS -->
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<br>
<p>Use this system of equations to answer questions 7-9.</p>
<blockquote>
<p>\( \begin{cases} 2d = 8f \\ 18 - 4f = 2d \end{cases} \)</p>
</blockquote>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="9d1ec316-6568-402b-8a36-13ff05fb3248" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="8ce6e32e-2f46-4628-ba5b-daa3c7b9ccb0" data-problem-comparator="integer" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li>What is the \(d\) 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>
<!--Q8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9193d0c7-22fb-4ca5-a356-5ecd109eacbf" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li>What is the \(f\) 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> \(\frac32\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!-- END TEXT ENTRY WITH REVEAL -->
<!-- BEGIN CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q9-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="9">
<li>Explain your solution.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal3">
<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
2d&=&8f
\\ d&=&4f
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
18-4f&=&2d
\\ 18-4f&=&2(4f)
\\ 18-4f&=&8f
\\ 18&=&12f
\\ \frac{18}{12}&=&f
\\ \frac32&=&f
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
2d&=&8(\frac32)
\\ 2d&=&12
\\ d&=&6
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN SIDE BY SIDE EQUATIONSS-->
<p>\(\begin{array}{rcr}
& & 18-4f=2d \\
2d=8f & & 18-4(\frac32)=2(6) \\
2(6)=8(\frac32) & & 18-(2)(3)=12 \\
12\overset?=(4)(3) & & 18-6=12 \\
12=12\checkmark & & 12=12\checkmark
\end{array}\) </p>
<!--END SIDE BY SIDE EQUATIONS -->
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<p>Use this system of equations to answer questions 10-12.</p>
<blockquote>
<p>\( \begin{cases} w + \frac17z = 4 \\ z = 3w -2 \end{cases} \)</p>
</blockquote>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="a01262f3-4563-4000-803f-3ec9071e0f76" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="7b3cebfa-349d-41c3-b87b-c80149441ef6" 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 \(w\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 3</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct 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>
<!-- END ACTIVITY INPUT 1 TRY -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="5f72bf47-6755-49bc-9a15-e0ea8d97a3b3" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q11-->
<div class="os-raise-ib-pset-problem" data-content-id="d4deb8ba-7cb4-4b57-8d73-8e7b37797294" data-problem-comparator="integer" data-problem-type="input" data-solution="7">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11">
<li>What is the \(z\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 7</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 7.</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 CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q12-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal4" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="12">
<li>Explain your solution.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal4">
<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
w+\frac17z&=&4
\\ w+\frac17(3w-2)&=&4
\\ 7w+3w-2&=&28
\\ 10w-2&=&28
\\ 10w&=&30
\\ w&=&3
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN ALIGN TO EQUALS -->
<p>\(\begin{array}{rcl}
z&=&3w-2
\\ z&=&3(3)-2
\\ z&=&9-2
\\ z&=&7
\\ \end{array}\)</p>
<!--END ALIGN TO EQUALS -->
<br>
<!--BEGIN SIDE BY SIDE EQUATIONSS-->
<p>\(\begin{array}{rcr}
w+\frac17z=4 & & z=3w-2 \\
3+\frac17(7)=4 & & 7=3(3)-2 \\
3+1\overset?=1=4 & & 7\overset?=1=9-2 \\
4=4 \checkmark & & 7=7 \checkmark \\
\end{array}\) </p>
<!--END SIDE BY SIDE EQUATIONS -->
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<h4>Extending Your Thinking</h4>
<p>Solve this system with four equations.</p>
<p>Use this system of equations to answer questions 1–4.</p>
<blockquote>\( \begin{cases}3 x + 2y - z + 5w= 20 \\ y = 2z-3w\\ z=w+1 \\ 2w=8 \end{cases} \)</blockquote>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="8c644827-aca3-4059-a327-bbd6d3d0424f" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="e7e035a3-3b18-46c1-97f2-b2ade9bcaaf2" data-problem-comparator="integer" data-problem-type="input" data-solution="3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<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! 3</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 3.</p>
</div>
</div>
<!--END QUESTION.-->
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<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
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</div>
</div>
<!-- END ACTIVITY INPUT 1 TRY -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="1efb4255-a110-4650-b5b2-46bf5538c849" 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="ee8d167f-4d01-41f8-a3e7-0ebee296816b" data-problem-comparator="integer" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<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! -2</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is -2.</p>
</div>
</div>
<!--END QUESTION.-->
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<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 -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="bafc3cb2-45ee-4b27-9b5e-8c18bac2c352" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="fec9bd23-0a98-4791-8846-fa412c54fe4c" 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="3">
<li>What is the \(z\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 5</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 5.</p>
</div>
</div>
<!--END QUESTION.-->
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<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
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</div>
</div>
<!-- END ACTIVITY INPUT 1 TRY -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="80d100c3-ca08-4211-b366-4d5a9a31dbb2" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="06683489-101e-452e-935f-97b24a2fd78b" data-problem-comparator="integer" data-problem-type="input" data-solution="4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>What is the \(w\) value?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 4</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 4.</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">
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</div>
</div>