11.8 Solving systems with cramer's rule  (Page 8/11)

$\begin{array}{l}0.5x-0.5y=10\hfill \\ -0.2y+0.2x=4\hfill \\ 0.1x+0.1z=2\hfill \end{array}$

$\begin{array}{r}\hfill 5x+3y-z=5\\ \hfill 3x-2y+4z=13\\ \hfill 4x+3y+5z=22\end{array}$

$\begin{array}{r}x+y+z=1\\ 2x+2y+2z=1\\ 3x+3y=2\end{array}$

$\begin{array}{l}2x-3y+z=\mathrm{-1}\hfill \\ x+y+z=\mathrm{-4}\hfill \\ 4x+2y-3z=33\hfill \end{array}$

$\begin{array}{l}3x+2y-z=\mathrm{-10}\hfill \\ x-y+2z=7\hfill \\ -x+3y+z=\mathrm{-2}\hfill \end{array}$

$\begin{array}{r}\hfill 3x+4z=\mathrm{-11}\\ \hfill x-2y=5\\ \hfill 4y-z=\mathrm{-10}\end{array}$

$\begin{array}{r}2x-3y+z=0\\ 2x+4y-3z=0\\ 6x-2y-z=0\end{array}$

$\begin{array}{r}6x-4y-2z=2\\ 3x+2y-5z=4\\ 6y-7z=5\end{array}$

Three odd numbers sum up to 61. The smaller is one-third the larger and the middle number is 16 less than the larger. What are the three numbers?

A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?

$\begin{array}{l}\begin{array}{l}\\ y=x^2-7\end{array}\hfill \\ y=5x-13\hfill \end{array}$

$\begin{array}{l}\begin{array}{l}\\ y=x^2-4\end{array}\hfill \\ y=5x+10\hfill \end{array}$

$\begin{array}{l}{x}^2+y^2=16\hfill \\ y=x-8\hfill \end{array}$

$\begin{array}{l}{x}^2+y^2=25\hfill \\ y=x^2+5\hfill \end{array}$

$\begin{array}{r}{x}^2+y^2=4\\ y-x^2=3\end{array}$

$y>x^2-1$

$\frac{1}{4}{x}^2+y^2<4$

$\begin{array}{l}{x}^2+y^2+2x<3\hfill \\ y>-x^2-3\hfill \end{array}$

$\begin{array}{l}{x}^2-2x+y^2-4x<4\hfill \\ y<-x+4\hfill \end{array}$

$\begin{array}{l}{x}^2+y^2<1\hfill \\ y^2<x\hfill \end{array}$

$\frac{-2x+6}{x^2+3x+2}$

$\frac{10x+2}{4x^2+4x+1}$

$\frac{7x+20}{x^2+10x+25}$

$\frac{x-18}{x^2-12x+36}$

$\frac{-x^2+36x+70}{x^3-125}$

$\frac{-5x^2+6x-2}{x^3+27}$

$\frac{x^3-4x^2+3x+11}{{(x^2-2)}^2}$

$\frac{4x^4-2x^3+22x^2-6x+48}{x{(x^2+4)}^2}$

$-4A$

$10D-6E$

$B+C$

$AB$

$BA$

$BC$

$CB$

$DE$

$ED$

$EC$

$CE$

$A^3$

$\left[\begin{array}{rrr}\hfill 1& \hfill 0& \hfill \mathrm{-3}\\ \hfill 0& \hfill 1& \hfill 2\\ \hfill 0& \hfill 0& \hfill 0\end{array}|\begin{array}{r}\hfill 7\\ \hfill \mathrm{-5}\\ \hfill 0\end{array}\right]$

$\left[\begin{array}{rrr}\hfill 1& \hfill 0& \hfill 5\\ \hfill 0& \hfill 1& \hfill \mathrm{-2}\\ \hfill 0& \hfill 0& \hfill 0\end{array}|\begin{array}{r}\hfill \mathrm{-9}\\ \hfill 4\\ \hfill 3\end{array}\right]$

$\begin{array}{l}\\ \begin{array}{r}\hfill -2x+2y+z=7\\ \hfill 2x-8y+5z=0\\ \hfill 19x-10y+22z=3\end{array}\end{array}$

$\begin{array}{l}4x+2y-3z=14\hfill \\ -12x+3y+z=100\hfill \\ 9x-6y+2z=31\hfill \end{array}$

$\begin{array}{r}\hfill x+3z=12\\ \hfill -x+4y=0\\ \hfill y+2z=-7\end{array}$

$\begin{array}{r}3x-4y=-7\\ -6x+8y=14\end{array}$

$\begin{array}{r}3x-4y=1\\ -6x+8y=6\end{array}$

$\begin{array}{l}\begin{array}{l}\\ -1.1x-2.3y=6.2\end{array}\hfill \\ -5.2x-4.1y=4.3\hfill \end{array}$

$\begin{array}{r}\hfill 2x+3y+2z=1\\ \hfill -4x-6y-4z=-2\\ \hfill 10x+15y+10z=0\end{array}$

$\begin{array}{r}\hfill -x+2y-4z=8\\ \hfill 3y+8z=-4\\ \hfill -7x+y+2z=1\end{array}$

$\left[\begin{array}{rr}\hfill -0.2& \hfill 1.4\\ \hfill 1.2& \hfill -0.4\end{array}\right]$

$\left[\begin{array}{rr}\hfill \frac{1}{2}& \hfill -\frac{1}{2}\\ \hfill -\frac{1}{4}& \hfill \frac{3}{4}\end{array}\right]$

$\left[\begin{array}{ccc}12& 9& -6\\ -1& 3& 2\\ -4& -3& 2\end{array}\right]$

$\left[\begin{array}{ccc}2& 1& 3\\ 1& 2& 3\\ 3& 2& 1\end{array}\right]$