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

 Page 9 / 11

For the following exercises, find the solutions by computing the inverse of the matrix.

$\begin{array}{l}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.3x-0.1y=-10\hfill \\ -0.1x+0.3y=14\hfill \end{array}$

$\left(-20,40\right)$

$\begin{array}{l}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.4x-0.2y=-0.6\hfill \\ -0.1x+0.05y=0.3\hfill \end{array}$

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

$\left(-1,0.2,0.3\right)$

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

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

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?

17% oranges, 34% bananas, 39% apples

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? ## Solving Systems with Cramer's Rule For the following exercises, find the determinant. $|\begin{array}{cc}100& 0\\ 0& 0\end{array}|$ 0 $|\begin{array}{cc}0.2& -0.6\\ 0.7& -1.1\end{array}|$ $|\begin{array}{ccc}-1& 4& 3\\ 0& 2& 3\\ 0& 0& -3\end{array}|$ 6 $|\begin{array}{ccc}\sqrt{2}& 0& 0\\ 0& \sqrt{2}& 0\\ 0& 0& \sqrt{2}\end{array}|$ For the following exercises, use Cramer’s Rule to solve the linear systems of equations. $\begin{array}{r}\hfill 4x-2y=23\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill -5x-10y=-35\end{array}$ $\left(6,\frac{1}{2}\right)$ $\begin{array}{l}0.2x-0.1y=0\\ -0.3x+0.3y=2.5\end{array}$ $\begin{array}{r}\hfill -0.5x+0.1y=0.3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill -0.25x+0.05y=0.15\end{array}$ ( x , 5 x + 3) $\begin{array}{l}x+6y+3z=4\\ 2x+y+2z=3\\ 3x-2y+z=0\end{array}$ $\begin{array}{r}\hfill 4x-3y+5z=-\frac{5}{2}\\ \hfill 7x-9y-3z=\frac{3}{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill x-5y-5z=\frac{5}{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}$ $\left(0,0,-\frac{1}{2}\right)$ $\begin{array}{r}\frac{3}{10}x-\frac{1}{5}y-\frac{3}{10}z=-\frac{1}{50}\\ \frac{1}{10}x-\frac{1}{10}y-\frac{1}{2}z=-\frac{9}{50}\\ \frac{2}{5}x-\frac{1}{2}y-\frac{3}{5}z=-\frac{1}{5}\end{array}$ ## Practice test Is the following ordered pair a solution to the system of equations? $\begin{array}{l}\\ \begin{array}{l}-5x-y=12\text{\hspace{0.17em}}\hfill \\ x+4y=9\hfill \end{array}\end{array}$ with $\text{\hspace{0.17em}}\left(-3,3\right)$ Yes For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists. $\begin{array}{r}\frac{1}{2}x-\frac{1}{3}y=4\\ \frac{3}{2}x-y=0\end{array}$ $\begin{array}{r}\hfill \begin{array}{l}\\ -\frac{1}{2}x-4y=4\end{array}\\ \hfill 2x+16y=2\end{array}$ No solutions exist. $\begin{array}{r}\hfill 5x-y=1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill -10x+2y=-2\end{array}$ $\begin{array}{l}4x-6y-2z=\frac{1}{10}\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x-7y+5z=-\frac{1}{4}\hfill \\ 3x+6y-9z=\frac{6}{5}\hfill \end{array}$ $\frac{1}{20}\left(10,5,4\right)$ $\begin{array}{r}x+z=20\\ x+y+z=20\\ x+2y+z=10\end{array}$ $\begin{array}{r}5x-4y-3z=0\\ 2x+y+2z=0\\ x-6y-7z=0\end{array}$ $\left(x,\frac{16x}{5}-\frac{13x}{5}\right)$ $\begin{array}{l}y={x}^{2}+2x-3\\ y=x-1\end{array}$ $\begin{array}{l}{y}^{2}+{x}^{2}=25\\ {y}^{2}-2{x}^{2}=1\end{array}$ $\left(-2\sqrt{2},-\sqrt{17}\right),\left(-2\sqrt{2},\sqrt{17}\right),\left(2\sqrt{2},-\sqrt{17}\right),\left(2\sqrt{2},\sqrt{17}\right)$ For the following exercises, graph the following inequalities. $y<{x}^{2}+9$ $\begin{array}{l}{x}^{2}+{y}^{2}>4\\ y<{x}^{2}+1\end{array}$ For the following exercises, write the partial fraction decomposition. $\frac{-8x-30}{{x}^{2}+10x+25}$ $\frac{13x+2}{{\left(3x+1\right)}^{2}}$ $\frac{5}{3x+1}-\frac{2x+3}{{\left(3x+1\right)}^{2}}$ $\frac{{x}^{4}-{x}^{3}+2x-1}{x{\left({x}^{2}+1\right)}^{2}}$ For the following exercises, perform the given matrix operations. $5\left[\begin{array}{cc}4& 9\\ -2& 3\end{array}\right]+\frac{1}{2}\left[\begin{array}{cc}-6& 12\\ 4& -8\end{array}\right]$ $\left[\begin{array}{cc}17& 51\\ -8& 11\end{array}\right]$ ${\left[\begin{array}{rr}\hfill \frac{1}{2}& \hfill \frac{1}{3}\\ \hfill \frac{1}{4}& \hfill \frac{1}{5}\end{array}\right]}^{-1}$ $\left[\begin{array}{cc}12& -20\\ -15& 30\end{array}\right]$ $\mathrm{det}|\begin{array}{cc}0& 0\\ 400& 4\text{,}000\end{array}|$ $\mathrm{det}|\begin{array}{rrr}\hfill \frac{1}{2}& \hfill -\frac{1}{2}& \hfill 0\\ \hfill -\frac{1}{2}& \hfill 0& \hfill \frac{1}{2}\\ \hfill 0& \hfill \frac{1}{2}& \hfill 0\end{array}|$ $-\frac{1}{8}$ If $\text{\hspace{0.17em}}\mathrm{det}\left(A\right)=-6,\text{\hspace{0.17em}}$ 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. $\begin{array}{l}14x-2y+13z=140\hfill \\ -2x+3y-6z=-1\hfill \\ x-5y+12z=11\hfill \end{array}$ Rewrite the augmented matrix as a system of linear equations. $\left[\begin{array}{rrr}\hfill 1& \hfill 0& \hfill 3\\ \hfill -2& \hfill 4& \hfill 9\\ \hfill -6& \hfill 1& \hfill 2\end{array}|\begin{array}{r}\hfill 12\\ \hfill -5\\ \hfill 8\end{array}\right]$ For the following exercises, use Gaussian elimination to solve the systems of equations. $\begin{array}{r}x-6y=4\\ 2x-12y=0\end{array}$ No solutions exist. $\begin{array}{r}\hfill 2x+y+z=-3\\ \hfill x-2y+3z=6\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill x-y-z=6\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}$ For the following exercises, use the inverse of a matrix to solve the systems of equations. $\begin{array}{r}\hfill 4x-5y=-50\\ \hfill -x+2y=80\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}$ $\left(100,90\right)$ $\begin{array}{r}\hfill \frac{1}{100}x-\frac{3}{100}y+\frac{1}{20}z=-49\\ \hfill \frac{3}{100}x-\frac{7}{100}y-\frac{1}{100}z=13\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\\ \hfill \frac{9}{100}x-\frac{9}{100}y-\frac{9}{100}z=99\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\end{array}$ For the following exercises, use Cramer’s Rule to solve the systems of equations. $\begin{array}{l}200x-300y=2\\ 400x+715y=4\end{array}$ $\left(\frac{1}{100},0\right)$ $\begin{array}{l}0.1x+0.1y-0.1z=-1.2\\ 0.1x-0.2y+0.4z=-1.2\\ 0.5x-0.3y+0.8z=-5.9\end{array}$ For the following exercises, solve using a system of linear equations. A factory producing cell phones has the following cost and revenue functions: $\text{\hspace{0.17em}}C\left(x\right)={x}^{2}+75x+2\text{,}688\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}R\left(x\right)={x}^{2}+160x.\text{\hspace{0.17em}}$ What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit. 32 or more cell phones per day 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 $1,050. How many of each type of ticket was sold? #### Questions & Answers By the definition, is such that 0!=1.why? Unikpel Reply (1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin\$)
hatdog
Mark
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
bsc F. y algebra and trigonometry pepper 2
given that x= 3/5 find sin 3x
4
DB
remove any signs and collect terms of -2(8a-3b-c)
-16a+6b+2c
Will
Joeval
(x2-2x+8)-4(x2-3x+5)
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
master
Soo sorry (5±Root11* i)/3
master
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
A banana.
Yaona
a function
Daniel
a function
emmanuel
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda