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<p><strong><em> Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<p>1. Solve</p>
<p>\( \left\{ \begin{array}{c l} –2x + 5y = –42\\ 7x + 2y = 30 \end{array}\right. \)</p>
<ul>
<li>\((0,15)\)</li>
<li>\((11,−4)\)</li>
<li>\((1,−8)\)</li>
<li>\((6,−6)\)</li>
</ul>
<p><strong>Answer: </strong>\( (6,-6)\)</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 -->
\(\begin{array}{rcl}7(6)+2y&=&30
\\42+2y&=&30
\\2y&=&-12
\\y&=&-6
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((6,-6)\).</p>
<br>
<!-- ENd WORKED SOLUTION 1-->
<p>2. Solve</p>
<p>\( \left\{ \begin{array}{c l} 6x – 5y = –34\\ 2x + 6y = 4 \end{array}\right. \)</p>
<ul>
<li>\((2,0)\)</li>
<li>\((1,8)\)</li>
<li>\((−4,2)\)</li>
<li>\((−9,−4)\)</li>
</ul>
<p><strong>Answer: </strong>\( (-4,2)\)</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 -->
\(\begin{array}{rcl}2x+6(2)&=&4
\\2x+12&=&4
\\2x&=&-8
\\x&=&-4
\\\end{array}\)<br><br>
<!--END ALIGN TO EQUALS -->
The solution is \((-4,2)\).</p>
<br>
<!-- ENd WORKED SOLUTION 2-->
<p>3. Solve<br></p>
<p>\( \left\{ \begin{array}{c l} 5x – y = –2.6\\ −4x − 6y = 1.4 \end{array}\right. \)</p>
<ul>
<li>\((7,–4.9)\)</li>
<li>\((0.5,0.1)\)</li>
<li>\((−3,−12)\)</li>
<li>\((−0.5,0.1)\)</li>
</ul>
<p><strong>Answer: </strong>\( (0.5,0.1)\)</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-->
<p>4. Solve</p>
<p>\( \left\{ \begin{array}{c l} 7x – 2y = 3\\ 4x + 5y = 3.25 \end{array}\right. \)</p>
<ul>
<li>\((1,2)\)</li>
<li>\((0.5,0.25)\)</li>
<li>\((–1,–5)\)</li>
<li>\((3,9)\)</li>
</ul>
<p><strong>Answer: </strong>\( (0.5,0.25)\)</p>
<!-- 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>5. Solve</p>
<p>\(\left\{\begin{array}{l}5x\;+\;9y\;=\;16\\x\;+\;2y\;=\;4\end{array}\right.\)</p>
<ul>
<li>\((−4,4)\)</li>
<li>\((3.2,0)\)</li>
<li>\((−8,6)\)</li>
<li>\((8,−2)\)</li>
</ul>
<p><strong>Answer: </strong>\( (-4,4)\)<br></p>
<!-- BEGIN WORKED SOLUTION 5-->
<p>\(-5(x + 2y=4)=-5x-10y=-20 \)<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>6. Solve</p>
<p>\( \left\{ \begin{array}{c l} \frac{3}{2}x - \frac{1}{4}y = 5\\ \frac{1}{3}x + \frac{1}{6}y = 2 \end{array}\right. \)</p>
<ul>
<li>\((4,4)\)</li>
<li>\((1,-5)\)</li>
<li>\( (-\frac{1}{5}, \frac{2}{3})\)</li>
<li>\((-4,-5)\)</li>
</ul>
<p><b>Answer:</b> (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-->
\(\begin{array}{r} 6x-y&=&20
\\ 2x+y&=&12
\\ \hline
8x&=&32
\\x&=&4
\end{array}\)<br>
<!--BEGIN ALIGN TO EQUALS WITH LINE-->
<!--BEGIN ALIGN TO EQUALS -->
<p>
\(\begin{align*}
2(4) + y &= 12 \\
8 + y &= 12 \\
y &= 4 \\
\end{align*}\)
</p>
<!--END ALIGN TO EQUALS -->
<p>The solution is \((4,4)\).</p>
<br>
<!-- ENd WORKED SOLUTION 6-->
<p>7. Solve
</p>
<p>\(\left\{\begin{array}{l}\frac13x\;+\;\frac19y\;=\;2\\–\;\frac12x\;+\;\frac45y\;=\;–3\end{array}\right.\)</p>
<ul>
<li>\((6,0)\)</li>
<li>\((7,−3)\)</li>
<li>\((8,−5)\)</li>
<li>\((−2,−5)\)</li>
</ul>
<p><b>Answer:</b>\( (6,0)\)</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-->
<p>8. Solve</p>
<p> \(\left\{\begin{array}{l}6x\;–\;8y\;=\;\frac{16}5\\3x\;+\;2y\;=\;\frac{14}5\end{array}\right.\)</p>
<ul>
<li>\((4,−4.6)\)</li>
<li>\((0,−0.4)\)</li>
<li>\((0.8,0.2)\)</li>
<li>\((2,1.1)\)</li>
</ul>
<p><b>Answer:</b> \((0.8,0.2)\)</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-->
<p>9. Solve</p>
<p>\(\left\{\begin{array}{l}5x\;–\;2y\;=\;2\\7x\;–\;4y\;=\;2.5\end{array}\right.\)</p>
<ul>
<li>\((2.4,5)\)</li>
<li>\((2,4)\)</li>
<li>\((0,−1)\)</li>
<li>\((0.5,0.25)\)</li>
</ul>
<p><b>Answer: </b>(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-->
<p>10. Solve</p>
<p>\(\left\{\begin{array}{l}\frac12x\;+\;\frac13y\;=\;\frac13\\\frac13x\;+\;\frac14y\;=\;-\frac18\end{array}\right.\)<br></p>
<ul>
<li>\((9,–12.5)\)</li>
<li>\((0,1)\)</li>
<li>\((6,–8)\)</li>
<li>\((12,–17)\)</li>
</ul>
<p><b>Answer: </b>\((9,–12.5) \)</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 -->