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<p>Complete the following questions to practice the skills you have learned in this lesson.<br></p>
<p>Solve each system of equations to practice the skills you have learned in this lesson. Enter your answer as “(x,y)” in the space provided. If any coordinate is a non-integer, enter it in decimal format.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="2244dfe1-81f1-49a0-ac96-3d6b4612b4b8" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--Q1-->
<div class="os-raise-ib-pset-problem" data-content-id="9bc99444-8aaa-47fe-a206-b69c41414c38" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((6,−6)\)" data-solution-options='["\\((0,15)\\)", "\\((11,−4)\\)", "\\((1,−8)\\)", "\\((6,−6)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>1. \( \left\{ \begin{array}{c l} –2x + 5y = –42\\ 7x + 2y = 30 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (6,−6)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2. Revisit</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (6,−6).
</p>
<!-- BEGIN WORKED SOLUTION 1-->
<p>\(- 2( –2x+5y=–42)=4x-10y=84 \)<br><br>
\(5(7x+2y=30)=35x+10y=150\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r}4x-10y&=&84
\\35x+10y&=&150
\\ \hline
39x&=&234
\\x&=&6
\end{array}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{array}{rcl}7x+8y&=&4
\\7(6)+2y&=&30
\\42+2y&=&30
\\2y&=&-12
\\y&=&-6
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((6,-6)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 1-->
</div>
</div>
<!--END QUESTION.-->
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="2d665fcc-760f-4664-95f6-6652b9a78b16" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((−4,2)\)" data-solution-options='["\\((2,0)\\)", "\\((1,8)\\)", "\\((−4,2)\\)", "\\((−9,−4)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>2. \( \left\{ \begin{array}{c l} 6x – 5y = –34\\ 2x + 6y = 4 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (−4,2)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (−4,2).
</p>
<!-- BEGIN WORKED SOLUTION 2-->
<p>\(- 3( 2x+6y=4)=-6x-18y=-12 \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r}6x–5y&=&34
\\-6x-18y&=&12
\\ \hline
-23y&=&-46
\\y&=&2
\end{array}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{array}{rcl}7x+8y&=&4
\\2x+6(2)&=&4
\\2x+12&=&4
\\2x&=&-8
\\x&=&-4
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((-4,2)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 2-->
</div>
</div>
<!--END QUESTION.-->
<!--Q3-->
<div class="os-raise-ib-pset-problem" data-content-id="34358845-9f4c-49dd-9744-40f69306892c" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((−0.5,0.1)\)" data-solution-options='["\\((7,–4.9)\\)", "\\((0.5,0.1)\\)", "\\((−3,−12)\\)", "\\((−0.5,0.1)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>3. \( \left\{ \begin{array}{c l} 5x – y = –2.6\\ −4x − 6y = 1.4 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (−0.5,0.1)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2. Revisit
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (−0.5,0.1).
</p>
<!-- BEGIN WORKED SOLUTION 3-->
<p>\(- 6( 5x–y=–2.6)=-30x+6y=15.6 \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r}-30x+6y&=&15.6
\\−4x−6y&=&1.4
\\ \hline
-34x&=&17
\\x&=&-0.5
\end{array}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{array}{rcl}−4(-0.5)−6y&=&1.4
\\2-6y&=&1.4
\\-6y&=&-0.6
\\y&=&0.1
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((-0.5,0.1)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 3-->
</div>
</div>
<!--END QUESTION.-->
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="d5da2e2a-5854-4af4-9134-d43fb40d9570" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((0.5,0.25)\)" data-solution-options='["\\((1,2)\\)", "\\((0.5,0.25)\\)", "\\((–1,–5)\\)", "\\((3,9)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>4. \( \left\{ \begin{array}{c l} 7x – 2y = 3\\ 4x + 5y = 3.25 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (0.5,0.25)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (0.5,0.25).
<!-- BEGIN WORKED SOLUTION 4-->
<p>\(5( 7x–2y=3)=35x-10y=15 \)<br><br>
\(2(4x+5y=3.25)=8x+10y=6.5 \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r}35x-10y&=&15
\\8x+10y&=&6.5
\\ \hline
43x&=&21.5
\\x&=&0.5
\end{array}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{array}{rcl}−4(0.5)+5y&=&3.25
\\2+5y&=&3.25
\\5y&=&1.25
\\y&=&0.25
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((0.5,0.25)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 4-->
</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q5-->
<div class="os-raise-ib-pset-problem" data-content-id="7d8cc503-792c-4f17-abd4-ca9cc3a74d71" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((−4,4)\)" data-solution-options='["\\((−4,4)\\)", "\\((3.2,0)\\)", "\\((−8,6)\\)", "\\((8,−2)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>5. \( \left\{ \begin{array}{c l} 5x + 9y = 16\\ x + 2y = 4 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (−4,4)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.3.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (−4,4).
<!-- BEGIN WORKED SOLUTION 5-->
<p>\(5( 7x–2y=3)=35x-10y=15 \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r}5x+9y&=&16
\\-5x-10y&=&-20
\\ \hline
-y&=&-4
\\y&=&4
\end{array}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{array}{rcl}x+2(4)&=&4
\\x+8&=&4
\\x&=&-4
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((-4,4)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 5-->
</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q6-->
<div class="os-raise-ib-pset-problem" data-content-id="ffdacaf7-13f0-460e-8e9c-95b0d3445bd8" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((4,4)\)" data-solution-options='["\\((4,4)\\)", "\\((1,−5)\\)", "\\((−\\frac15,\\frac23)\\)", "\\((−4,−5)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>6. \( \left\{ \begin{array}{c l} \frac{3}{2}x - \frac{1}{4}y = 5\\ \frac{1}{3}x + \frac{1}{6}y = 2 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \( (4,4) \)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.3.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \( (4,4) \).
</p>
<!-- BEGIN WORKED SOLUTION 6-->
<p>\( 4( \frac32 x-\frac14 y=5)=6x-y=20\)<br><br>
<p>\(6( \frac13 x+\frac16 y=2)=2x+y=12\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{array}{r} 6x-y&=&5
\\ 2x+y&=&12
\\ \hline
8x&=&32
\\x&=&4
\end{array}\)<br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
<p>
\(\begin{align*}
x + 2(4)y &= 12 \\
8 + y &= 12 \\
y &= 4 \\
\end{align*}\)
</p>
<!--END ALIGN TO EQUALS -->
<p>The solution is \((4,4)\).</p>
<br>
<!-- ENd WORKED SOLUTION 6-->
</p>
</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="acd91d7d-e4a8-45d6-b064-706857b5cc44" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((6,0)\)" data-solution-options='["\\((6,0)\\)", "\\((7,−3)\\)", "\\((8,−5)\\)", "\\((−2,−5)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>7. \( \left\{ \begin{array}{c l} \frac{1}{3}x + \frac{1}{9}y = 2\\ -\frac{1}{2}x + \frac{4}{5}y = -3 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (6,0)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.3.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (6,0).
</p>
<!-- BEGIN WORKED SOLUTION 7-->
<p>\(9( \frac13 x+ \frac19 y=2)=3x+y=18 \)<br><br>
\(10( –\frac12 x+ \frac45 y=–3)=-5x+8y=-30 \)<br><br>
\(-8( 3x+y=18)=-24x-8y=-144 \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{align*}-5x+8y&=-30
\\-24x-8y&=-144
\\ \hline
-29x&=-174
\\x&=6
\\\end{align*}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{align*}3x+y&=18
\\(3(6)+y&=18
\\18+y&=18
\\y&=0
\\\end{align*}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((6,0)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 7-->
</div>
</div>
<!--END QUESTION.-->
<!--Q8-->
<div class="os-raise-ib-pset-problem" data-content-id="786245a2-01a9-446a-9503-4d7bea9acdba" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((0.8,0.2)\)" data-solution-options='["\\((4,−4.6)\\)", "\\((0,−0.4)\\)", "\\((0.8,0.2)\\)", "\\((2,1.1)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>8. \( \left\{ \begin{array}{c l} 6x - 8y = \frac{16}{5}\\ 3x + 2y = \frac{14}{5} \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (0.8,0.2)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (0.8,0.2).
</p>
<!-- BEGIN WORKED SOLUTION 8-->
<p>\( 4( 3x+2y=\frac{14}{5})=12x+8y=\frac{56}{5} \)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{align*}6x-8y&=\frac{16}{5}
\\12x+8y&=\frac{56}{5}
\\ \hline
18x&=\frac{72}{5}
\\90x&=72
\\x&=\frac{72}{90}
\\x&=\frac{4}{5}
\\x&=0.8
\\\end{align*}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{align*}3(\frac45)+2y&=\frac{14}{5}
\\\frac{12}{5}+2y&=\frac{14}{5}
\\5(\frac{12}{5}+2y&=\frac{14}{5})
\\12+10y&=14
\\10y&=2
\\y&=\frac{2}{10}
\\y&=\frac15
\\y&=0.2
\\\end{align*}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((0.8,0.2)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 8-->
</div>
</div>
<!--END QUESTION.-->
<!--Q9-->
<div class="os-raise-ib-pset-problem" data-content-id="b2357ec1-f9da-4c47-98f6-69f02e394cc1" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((0.5,0.25)\)" data-solution-options='["\\((2.4,5)\\)", "\\((2,4)\\)", "\\((0,−1)\\)", "\\((0.5,0.25)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>9. \( \left\{ \begin{array}{c l} 5x – 2y = 2 \\ 7x – 4y = 2.5 \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (0.5,0.25)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.2.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (0.5,0.25).
</p>
<!-- BEGIN WORKED SOLUTION 9-->
<p>\(-2(5x-2y=2)=-10x+4y=-4\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{align*}-10x+4y&=-4
\\7x-4y&=2.5
\\ \hline
-3x&=-1.5
\\x&=0.5
\end{align*}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{align*}5(0.5)-2y&=2
\\2.5-2y&=2
\\-2y&=-0.5
\\y&=0.25
\\\end{align*}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((0.5,0.25)\).
</p>
<br>
<!-- ENd WORKED SOLUTION 9-->
</div>
</div>
<!--END QUESTION.-->
<!--Q10-->
<div class="os-raise-ib-pset-problem" data-content-id="326adc26-1990-4c2e-93b2-252ca0784e1d" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((9,–12.5)\)" data-solution-options='["\\((9,–12.5)\\)", "\\((0,1)\\)", "\\((6,–8)\\)", "\\((12,–17)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>10. \( \left\{ \begin{array}{c l} \frac{1}{2}x + \frac{1}{3}y = \frac{1}{3}\\ \frac{1}{3}x + \frac{1}{4}y = -\frac{1}{8} \end{array}\right. \)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! (9,–12.5)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 2.6.3.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is (9,–12.5).
</p>
<!-- BEGIN WORKED SOLUTION -->
<p>\(6( \frac12 x+\frac13 y=\frac13)=3x+2y=2 \)<br><br>
\(24( \frac13 x+\frac14 y=–\frac18)=8x+6y=-3 \)<br><br>
\(-3(3x+2y=2)=-9x-6y=-6\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
\(\begin{align*}-9x-6y&=-6
\\8x+6y&=-3
\\ \hline
-x&=-9
\\x&=9
\\\end{align*}\)<br><br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
\(\begin{align*}3(9)+2y&=2
\\27+2y&=2
\\2y&=-25
\\y=&-12.5
\\\end{align*}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((9,-12.5)\).
</p>
<br>
<!-- ENd WORKED SOLUTION -->
</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>