Answer Key 5.2
- \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\
-3x&=&6x&-&9 \\
-6x&&-6x&& \\
\hline
\dfrac{-9x}{-9}&=&\dfrac{-9}{-9}&& \\ \\
x&=&1&& \\ \\
\therefore y&=&-3(1)&& \\
y&=&-3&& \\ \\
(1,-3)&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
x&+&5&=&-2x&-&4 \\
+2x&-&5&&+2x&-&5 \\
\hline
&&\dfrac{3x}{3}&=&\dfrac{-9}{3}&& \\ \\
&&x&=&-3&& \\ \\
&&\therefore y&=&-3&+&5 \\
&&y&=&2&& \\ \\
(-3,2)&&&&&& \\
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
2x&-&1&=&-2x&-&9 \\
+2x&+&1&&+2x&+&1 \\
\hline
&&\dfrac{4x}{4}&=&\dfrac{-8}{4}&& \\ \\
&&x&=&-2&& \\ \\
&&\therefore y&=&2(-2)&-&1 \\
&&y&=&-4&-&1 \\
&&y&=&-5&& \\
(-2,-5)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\
6x&+&3&=&-6x&+&3 \\
+6x&-&3&&+6x&-&3 \\
\hline
&&\dfrac{12x}{12}&=&\dfrac{0}{12}&& \\ \\
&&x&=&0&& \\ \\
&&\therefore y&=&6(0)&+&3 \\
&&y&=&3&& \\
(0,3)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
6x&+&4&=&-3x&-&5 \\
+3x&-&4&&+3x&-&4 \\
\hline
&&\dfrac{9x}{9}&=&\dfrac{-9}{9}&& \\ \\
&&x&=&-1&& \\ \\
&&\therefore y&=&6(-1)&+&4 \\
&&y&=&-6&+&4 \\
&&y&=&-2&& \\
(-1,-2)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
3x&+&13&=&-2x&-&22 \\
+2x&-&13&&+2x&-&13 \\
\hline
&&\dfrac{5x}{5}&=&\dfrac{-35}{5}&& \\ \\
&&x&=&-7&& \\ \\
&&\therefore y&=&3(-7)&+&13 \\
&&y&=&-21&+&13 \\
&&y&=&-8&& \\
(-7,-8)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
3x&+&2&=&-3x&+&8 \\
+3x&-&2&&+3x&-&2 \\
\hline
&&\dfrac{6x}{6}&=&\dfrac{6}{6}&& \\ \\
&&x&=&1&& \\ \\
&&\therefore y&=&3(1)&+&2 \\
&&y&=&3&+&2 \\
&&y&=&5&& \\
(1,5)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-2x&-&9&=&-5x&-&21 \\
+5x&+&9&&+5x&+&9 \\
\hline
&&\dfrac{3x}{3}&=&\dfrac{-12}{3}&& \\ \\
&&x&=&-4&& \\ \\
&&\therefore y&=&-2(-4)&-&9 \\
&&y&=&8&-&9 \\
&&y&=&-1&& \\
(-4,-1)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
2x&-&3&=&-2x&+&9 \\
+2x&+&3&&+2x&+&3 \\
\hline
&&\dfrac{4x}{4}&=&\dfrac{12}{4}&& \\ \\
&&x&=&3&& \\ \\
&&\therefore y&=&2(3)&-&3 \\
&&y&=&6&-&3 \\
&&y&=&3&& \\
(3,3)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
7x&-&24&=&-3x&+&16 \\
+3x&+&24&&+3x&+&24 \\
\hline
&&\dfrac{10x}{10}&=&\dfrac{40}{10}&& \\ \\
&&x&=&4&& \\ \\
&&\therefore y&=&7(4)&-&24 \\
&&y&=&28&-&24 \\
&&y&=&4&& \\
(4,4)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
3x&-&3(3x&-&4)&=&-6 \\
3x&-&9x&+&12&=&-6 \\
&&&-&12&&-12 \\
\hline
&&&&\dfrac{-6x}{-6}&=&\dfrac{-18}{-6} \\ \\
&&&&x&=&3 \\ \\
&&&&\therefore y&=&3(3)-4 \\
&&&&y&=&9-4 \\
&&&&y&=&5 \\
(3,5)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-x&+&3(6x&+&21)&=&\phantom{-}12 \\
-x&+&18x&+&63&=&\phantom{-}12 \\
&&&-&63&&-63 \\
\hline
&&&&\dfrac{17x}{17}&=&\dfrac{-51}{17} \\ \\
&&&&x&=&-3 \\ \\
&&&&\therefore y&=&6(-3)+21 \\
&&&&y&=&-18+21 \\
&&&&y&=&3 \\
(-3,3)&&&&&&
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\
3x&-&6(-6)&=&30 \\
3x&+&36&=&30 \\
&-&36&&-36 \\
\hline
&&\dfrac{3x}{3}&=&\dfrac{-6}{3} \\ \\
&&x&=&-2 \\ \\
&&y&=&-6 \\
(-2,-6)&&&& \\
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
6x&-&4(-6x&+&2)&=&-8 \\
6x&+&24x&-&8&=&-8 \\
&&&+&8&&+8 \\
\hline
&&&&\dfrac{30x}{30}&=&\dfrac{0}{30} \\ \\
&&&&\therefore x&=&0 \\ \\
&&&&\therefore y&=&-6(0)+2 \\
&&&&y&=&0+2 \\
&&&&y&=&2 \\
(0,2)&&&&&&
\end{array}\) - \(\begin{array}{rrrrr}
\\ \\ \\ \\ \\ \\ \\ \\ \\
3x&+&4(-5)&=&-17 \\
3x&-&20&=&-17 \\
&+&20&&+20 \\
\hline
&&\dfrac{3x}{3}&=&\dfrac{3}{3} \\ \\
&&x&=&1 \\ \\
&&y&=&-5 \\
(1,-5)&&&& \\
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
7x&+&2(5x&+&5)&=&-7 \\
7x&+&10x&+&10&=&-7 \\
&&&-&10&&-10 \\
\hline
&&&&\dfrac{17x}{17}&=&\dfrac{-17}{17} \\ \\
&&&&x&=&-1 \\ \\
&&&&\therefore y&=&5(-1)+5 \\
&&&&y&=&-5+5 \\
&&&&y&=&0 \\
(-1,0)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-6x&+&6y&=&-12&(\div &6) \\
-x&+&y&=&-2&& \\
+x&&&&+x&& \\
\hline
&&y&=&x&-&2 \\ \\
8x&-&3(x&-&2)&=&16 \\
8x&-&3x&+&6&=&16 \\
&&&-&6&&-6 \\
\hline
&&&&\dfrac{5x}{5}&=&\dfrac{10}{5} \\ \\
&&&&x&=&2 \\ \\
&&&&\therefore y&=&x-2 \\
&&&&y&=&2-2=0 \\
(2,0)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-8x&+&2y&=&-6&(\div &2) \\
-4x&+&y&=&-3&& \\
+4x&&&&+4x&& \\
\hline
&&y&=&4x&-&3 \\ \\
-2x&+&3(4x&-&3)&=&11 \\
-2x&+&12x&-&9&=&11 \\
&&&+&9&&+9 \\
\hline
&&&&\dfrac{10x}{10}&=&\dfrac{20}{10} \\ \\
&&&&x&=&2 \\ \\
&&&&\therefore y&=&4(2)-3 \\
&&&&y&=&8-3=5 \\
(2,5)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
-7x&-&y&=&20&& \\
-20&+&y&&-20&+&y \\
\hline
-7x&-&20&=&y&& \\ \\
2x&+&3(-7x&-&20)&=&\phantom{+}16 \\
2x&-&21x&-&60&=&\phantom{+}16 \\
&&&+&60&&+60 \\
\hline
&&&&\dfrac{-19x}{-19}&=&\dfrac{76}{-19} \\ \\
&&&&x&=&-4 \\ \\
&&&&\therefore y&=&-7(-4)-20 \\
&&&&y&=&28-20 \\
&&&&y&=&8 \\
(-4,8)&&&&&&
\end{array}\) - \(\begin{array}{rrrrrrrll}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
&&(-x&-&4y&=&-14)&(-1)& \\
&&x&+&4y&=&14&& \\
&&&-&4y&&-4y&& \\
\hline
&&&&x&=&14&-&4y \\ \\
&&(-6x&+&8y&=&12)&\div &2 \\
&&-3x&+&4y&=&6&& \\
-3(14&-&4y)&+&4y&=&6&& \\
-42&+&12y&+&4y&=&6&& \\
+42&&&&&&+42&& \\
\hline
&&&&\dfrac{16y}{16}&=&\dfrac{48}{16}&& \\ \\
&&&&y&=&3&& \\ \\
&&&&x&=&14&-&4(3) \\
&&&&x&=&14&-&12 \\
&&&&x&=&2&& \\
(2,3)&&&&&&&&
\end{array}\)
