11.8 Solving systems with cramer's rule  (Page 9/11)

$\begin{array}{l}0.3x-0.1y=-10\hfill \\ -0.1x+0.3y=14\hfill \end{array}$

$\begin{array}{l}0.4x-0.2y=-0.6\hfill \\ -0.1x+0.05y=0.3\hfill \end{array}$

$\begin{array}{r}4x+3y-3z=-4.3\\ 5x-4y-z=-6.1\\ x+z=-0.7\end{array}$

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

Students were asked to bring their favorite fruit to class. 90% of the fruits consisted of banana, apple, and oranges. If oranges were half as popular as bananas and apples were 5% more popular than bananas, what are the percentages of each individual fruit?

A sorority held a bake sale to raise money and sold brownies and chocolate chip cookies. They priced the brownies at $2 and the chocolate chip cookies at $1. They raised $250 and sold 175 items. How many brownies and how many cookies were sold?

$\left|\begin{array}{cc}100& 0\\ 0& 0\end{array}\right|$

$\left|\begin{array}{cc}0.2& -0.6\\ 0.7& -1.1\end{array}\right|$

$\left|\begin{array}{ccc}-1& 4& 3\\ 0& 2& 3\\ 0& 0& -3\end{array}\right|$

$\left|\begin{array}{ccc}\sqrt{2}& 0& 0\\ 0& \sqrt{2}& 0\\ 0& 0& \sqrt{2}\end{array}\right|$

$\begin{array}{r}\hfill 4x-2y=23\\ \hfill -5x-10y=-35\end{array}$

$\begin{array}{l}0.2x-0.1y=0\\ -0.3x+0.3y=2.5\end{array}$

$\begin{array}{r}\hfill -0.5x+0.1y=0.3\\ \hfill -0.25x+0.05y=0.15\end{array}$

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

$\begin{array}{r}\hfill 4x-3y+5z=-\frac{5}{2}\\ \hfill 7x-9y-3z=\frac{3}{2}\\ \hfill x-5y-5z=\frac{5}{2}\end{array}$

$\begin{array}{r}\frac{3}{10}x-\frac{1}{5}y-\frac{3}{10}z=-\frac{1}{50}\\ \frac{1}{10}x-\frac{1}{10}y-\frac{1}{2}z=-\frac{9}{50}\\ \frac{2}{5}x-\frac{1}{2}y-\frac{3}{5}z=-\frac{1}{5}\end{array}$

$\begin{array}{l}\\ \begin{array}{l}-5x-y=12\hfill \\ x+4y=9\hfill \end{array}\end{array}$ with $(-3,3)$

$\begin{array}{r}\frac{1}{2}x-\frac{1}{3}y=4\\ \frac{3}{2}x-y=0\end{array}$

$\begin{array}{r}\hfill \begin{array}{l}\\ -\frac{1}{2}x-4y=4\end{array}\\ \hfill 2x+16y=2\end{array}$

$\begin{array}{r}\hfill 5x-y=1\\ \hfill -10x+2y=-2\end{array}$

$\begin{array}{l}4x-6y-2z=\frac{1}{10}\hfill \\ x-7y+5z=-\frac{1}{4}\hfill \\ 3x+6y-9z=\frac{6}{5}\hfill \end{array}$

$\begin{array}{r}x+z=20\\ x+y+z=20\\ x+2y+z=10\end{array}$

$\begin{array}{r}5x-4y-3z=0\\ 2x+y+2z=0\\ x-6y-7z=0\end{array}$

$\begin{array}{l}y=x^2+2x-3\\ y=x-1\end{array}$

$\begin{array}{l}{y}^2+x^2=25\\ y^2-2x^2=1\end{array}$

$y<x^2+9$

$\begin{array}{l}{x}^2+y^2>4\\ y<x^2+1\end{array}$

$\frac{-8x-30}{x^2+10x+25}$

$\frac{13x+2}{{(3x+1)}^2}$

$\frac{x^4-x^3+2x-1}{x{(x^2+1)}^2}$

$5\left[\begin{array}{cc}4& 9\\ -2& 3\end{array}\right]+\frac{1}{2}\left[\begin{array}{cc}-6& 12\\ 4& -8\end{array}\right]$

$\left[\begin{array}{rrr}\hfill 1& \hfill 4& \hfill -7\\ \hfill -2& \hfill 9& \hfill 5\\ \hfill 12& \hfill 0& \hfill -4\end{array}\right]\left[\begin{array}{cc}3& -4\\ 1& 3\\ 5& 10\end{array}\right]$

${\left[\begin{array}{rr}\hfill \frac{1}{2}& \hfill \frac{1}{3}\\ \hfill \frac{1}{4}& \hfill \frac{1}{5}\end{array}\right]}^{-1}$

$\det \left|\begin{array}{cc}0& 0\\ 400& 4\text{,}000\end{array}\right|$

$\det \left|\begin{array}{rrr}\hfill \frac{1}{2}& \hfill -\frac{1}{2}& \hfill 0\\ \hfill -\frac{1}{2}& \hfill 0& \hfill \frac{1}{2}\\ \hfill 0& \hfill \frac{1}{2}& \hfill 0\end{array}\right|$

If $\det (A)=\mathrm{-6},$ what would be the determinant if you switched rows 1 and 3, multiplied the second row by 12, and took the inverse?

Rewrite the system of linear equations as an augmented matrix.

Rewrite the augmented matrix as a system of linear equations.

$\begin{array}{r}x-6y=4\\ 2x-12y=0\end{array}$

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

$\begin{array}{r}\hfill 4x-5y=-50\\ \hfill -x+2y=80\end{array}$

$\begin{array}{r}\hfill \frac{1}{100}x-\frac{3}{100}y+\frac{1}{20}z=-49\\ \hfill \frac{3}{100}x-\frac{7}{100}y-\frac{1}{100}z=13\\ \hfill \frac{9}{100}x-\frac{9}{100}y-\frac{9}{100}z=99\end{array}$

$\begin{array}{l}200x-300y=2\\ 400x+715y=4\end{array}$

$\begin{array}{l}0.1x+0.1y-0.1z=-1.2\\ 0.1x-0.2y+0.4z=-1.2\\ 0.5x-0.3y+0.8z=-5.9\end{array}$

A factory producing cell phones has the following cost and revenue functions: $C(x)=x^2+75x+2\text{,}688$ and $R(x)=x^2+160x.$ What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.

A small fair charges $1.50 for students, $1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of $1,050. How many of each type of ticket was sold?