[latexpage]

1. \(2x-y-2=0\)

   \(x\)	\(y\)
   0	−2
   1	0
   2	2

   \(2x+3y+6=0\)

   \(x\)	\(y\)
   0	−2
   −3	0
   −6	2

   

2. \(\phantom{1}\)
   \(x+y=2\Rightarrow x=2-y \\ \)
   \(\begin{array}{rrrrrrl}
   3(2&-&y)&-&4y&=&13 \\
   6&-&3y&-&4y&=&13 \\
   -6&&&&&&-6 \\
   \midrule
   &&&&-7y&=&\phantom{-}7 \\
   &&&&y&=&-1 \\ \\
   &&&&x&=&2--1 \\
   &&&&x&=&3
   \end{array}\)
   \((3,-1)\)
3. \(\begin{array}{rrrrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   &4x&-&3y&=&6 \\
   +&4x&+&3y&=&2 \\
   \midrule
   &&&8x&=&8 \\
   &&&x&=&1 \\ \\
   &3y&+&4(1)&=&2 \\
   &&-&4&&-4 \\
   \midrule
   &&&3y&=&-2 \\ \\
   &&&y&=&-\dfrac{2}{3}
   \end{array}\)
   \(\left(1,-\dfrac{2}{3}\right)\)
4. \(\begin{array}{ll}
   \begin{array}{rrrrrrrl}
   \\ \\ \\ \\ \\ \\ \\ \\
   \left[1\right]&(x&+&y&+&z&=&\phantom{-}6)(-2) \\
   \left[2\right]&&&(-2x&+&z&=&-3)(-1) \\ \\
   \left[1\right]&-2x&-&2y&-&2z&=&-12 \\
   +&&&2y&+&4z&=&\phantom{-}10 \\
   \midrule
   &&&-2x&+&2z&=&-2 \\
   +&&\left[2\right]&2x&-&z&=&\phantom{-}3 \\
   \midrule
   &&&&&z&=&1 \\
   \end{array}
   & \hspace{0.25in}
   \begin{array}{rrrrr}
   \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
   2y&+&4z&=&10 \\
   2y&+&4(1)&=&10 \\
   &-&4&&-4 \\
   \midrule
   &&2y&=&6 \\
   &&y&=&3 \\ \\
   -2x&+&z&=&-3 \\
   -2x&+&1&=&-3 \\
   &-&1&&-1 \\
   \midrule
   &&-2x&=&-4 \\
   &&x&=&2 \\
   \end{array}
   \end{array}\)
   \((2,3,1)\)
5. \(36+\{\cancel{-2x-\left[6x-3(5-2x)\right]\}^0}1+6x^3\)
   \(36+1+6x^3\Rightarrow 6x^3+37\)
6. \(6a^2b(a^2-9)\)
   \(6a^4b-54a^2b\)
7. \(\begin{array}{rrrrrlrrrr}
   \\ \\ \\ \\ \\ \\
   &x^2&+&3x&+&5&&&& \\
   \times &x^2&+&3x&+&5&&&& \\
   \midrule
   &x^4&+&3x^3&+&5x^2&&&& \\
   &&&3x^3&+&9x^2&+&15x&& \\
   +&&&&&5x^2&+&15x&+&25 \\
   \midrule
   &x^4&+&6x^3&+&19x^2&+&30x&+&25
   \end{array}\)
8. \(\polylongdiv{2x^4+x^3+4x^2-4x-5}{2x+1}\)
9. \(x^2-x+18x-18\)
   \(x(x-1)+18(x-1)\)
   \((x-1)(x+18)\)
10. \(2(a^2-2ab-15b^2)\)
    \(2(a^2-5ab+3ab-15b^2)\)
    \(2\left[a(a-5b)+3b(a-5b)\right]\)
    \(2(a-5b)(a+3b)\)
11. \((2x)^3-y^3\)
    \((2x-y)(4x^2+2xy+y^2)\)
12. \((4y^2-x^2)(4y^2+x^2)\)
    \((2y-x)(2y+x)(4y^2+x^2)\)
13. \(\phantom{1}\)
    \(B+S=30\Rightarrow B=30-S \\ \)
    \(\begin{array}{rrrrrrr}
    B&-&10&=&4(S&-&10) \\
    30-S&-&10&=&4S&-&40 \\
    +S&+&40&&+S&+&40 \\
    \midrule
    &&60&=&5S&& \\ \\
    &&S&=&\dfrac{60}{5}&=&12 \\ \\
    &&\therefore B&=&30&-&S \\
    &&B&=&30&-&12 \\
    &&B&=&18&&
    \end{array}\)
14. \(\begin{array}{rrrrrl}
    \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
    &(D&+&N&=&\phantom{1}18)(-1) \\
    &(10D&+&5N&=&120)(\div 5) \\ \\
    &-D&-&N&=&-18 \\
    +&2D&+&N&=&\phantom{-}24 \\
    \midrule
    &&&D&=&6 \\ \\
    \therefore &D&+&N&=&18 \\
    &6&+&N&=&18 \\
    &-6&&&&-6 \\
    \midrule
    &&&N&=&12
    \end{array}\)
15. \(\phantom{1}\)
    \(\text{if }x=5\%, \text{ then }10-x=30\% \\ \)
    \(\begin{array}{rrrrcrl}
    5x&+&30(10&-&x)&=&25(10) \\
    5x&+&300&-&30x&=&\phantom{-}250 \\
    &-&300&&&&-300 \\
    \midrule
    &&&&-25x&=&-50 \\ \\
    &&&&x&=&\dfrac{-50}{-25}\text{ or 2 L of 5\%} \\ \\
    &&10&-&x&=&\text{8 L of 30\%}
    \end{array}\)