7.1 Systems of linear equations: two variables  (Page 8/20)

$\begin{array}{c}5x-y=4\\ x+6y=2\end{array}$ and $(4,0)$

$\begin{array}{l}\mathrm{-3}x-5y=13\hfill \\ -x+4y=10\hfill \end{array}$ and $(\mathrm{-6},1)$

$\begin{array}{c}3x+7y=1\\ 2x+4y=0\end{array}$ and $(2,3)$

$\begin{array}{l}\mathrm{-2}x+5y=7\hfill \\ 2x+9y=7\hfill \end{array}$ and $(\mathrm{-1},1)$

$\begin{array}{c}x+8y=43\\ 3x\mathrm{-2}y=\mathrm{-1}\end{array}$ and $(3,5)$

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

$\begin{array}{l}3x\mathrm{-2}y=18\hfill \\ 5x+10y=\mathrm{-10}\hfill \end{array}$

$\begin{array}{l}4x+2y=\mathrm{-10}\\ 3x+9y=0\end{array}$

$\begin{array}{l}2x+4y=\mathrm{-3.8}\\ 9x\mathrm{-5}y=1.3\end{array}$

$\begin{array}{l}\hfill \\ \begin{array}{l}\\ \begin{array}{l}-2x+3y=1.2\hfill \\ -3x-6y=1.8\hfill \end{array}\end{array}\hfill \end{array}$

$\begin{array}{l}x\mathrm{-0.2}y=1\hfill \\ \mathrm{-10}x+2y=5\hfill \end{array}$

$\begin{array}{l}3x+5y=9\hfill \\ 30x+50y=\mathrm{-90}\hfill \end{array}$

$\begin{array}{l}\hfill \\ \begin{array}{l}\mathrm{-3}x+y=2\hfill \\ 12x\mathrm{-4}y=\mathrm{-8}\hfill \end{array}\hfill \end{array}$

$\begin{array}{l}\frac{1}{2}x+\frac{1}{3}y=16\\ \frac{1}{6}x+\frac{1}{4}y=9\end{array}$

$\begin{array}{l}\\ \begin{array}{l}-\frac{1}{4}x+\frac{3}{2}y=11\hfill \\ -\frac{1}{8}x+\frac{1}{3}y=3\hfill \end{array}\end{array}$

$\begin{array}{l}\hfill \\ \begin{array}{l}\mathrm{-2}x+5y=\mathrm{-42}\hfill \\ 7x+2y=30\hfill \end{array}\hfill \end{array}$

$\begin{array}{l}6x\mathrm{-5}y=\mathrm{-34}\\ 2x+6y=4\end{array}$

$\begin{array}{l}5x-y=\mathrm{-2.6}\hfill \\ \mathrm{-4}x\mathrm{-6}y=1.4\hfill \end{array}$

$\begin{array}{l}7x\mathrm{-2}y=3\\ 4x+5y=3.25\end{array}$

$\begin{array}{l}\hfill \\ \begin{array}{l}\mathrm{-x}+2y=\mathrm{-1}\hfill \\ 5x\mathrm{-10}y=6\hfill \end{array}\hfill \end{array}$

$\begin{array}{l}7x+6y=2\hfill \\ \mathrm{-28}x\mathrm{-24}y=\mathrm{-8}\hfill \end{array}$

$\begin{array}{l}\frac{5}{6}x+\frac{1}{4}y=0\\ \frac{1}{8}x-\frac{1}{2}y=-\frac{43}{120}\end{array}$

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

$\begin{array}{l}\hfill \\ \begin{array}{l}\mathrm{-0.2}x+0.4y=0.6\hfill \\ x\mathrm{-2}y=\mathrm{-3}\hfill \end{array}\hfill \end{array}$

$\begin{array}{l}\begin{array}{l}\\ \mathrm{-0.1}x+0.2y=0.6\end{array}\hfill \\ 5x\mathrm{-10}y=1\hfill \end{array}$

$\begin{array}{l}5x+9y=16\hfill \\ x+2y=4\hfill \end{array}$

$\begin{array}{l}6x\mathrm{-8}y=\mathrm{-0.6}\\ 3x+2y=0.9\end{array}$

$\begin{array}{l}5x\mathrm{-2}y=2.25\\ 7x\mathrm{-4}y=3\end{array}$

$\begin{array}{l}\begin{array}{l}\hfill \\ x-\frac{5}{12}y=-\frac{55}{12}\hfill \end{array}\hfill \\ \mathrm{-6}x+\frac{5}{2}y=\frac{55}{2}\hfill \end{array}$

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

$\begin{array}{l}3x+6y=11\\ 2x+4y=9\end{array}$

$\begin{array}{l}\frac{7}{3}x-\frac{1}{6}y=2\hfill \\ -\frac{21}{6}x+\frac{3}{12}y=\mathrm{-3}\hfill \end{array}$

$\begin{array}{l}\frac{1}{2}x+\frac{1}{3}y=\frac{1}{3}\\ \frac{3}{2}x+\frac{1}{4}y=-\frac{1}{8}\end{array}$

$\begin{array}{l}2.2x+1.3y=\mathrm{-0.1}\\ 4.2x+4.2y=2.1\end{array}$

$\begin{array}{l}0.1x+0.2y=2\hfill \\ 0.35x\mathrm{-0.3}y=0\hfill \end{array}$

$\begin{array}{l}3x-y=0.6\\ x\mathrm{-2}y=1.3\end{array}$

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

$\begin{array}{l}x+2y=7\hfill \\ 2x+6y=12\hfill \end{array}$

$\begin{array}{l}3x\mathrm{-5}y=7\hfill \\ x\mathrm{-2}y=3\hfill \end{array}$

$\begin{array}{l}3x\mathrm{-2}y=5\hfill \\ \mathrm{-9}x+6y=\mathrm{-15}\hfill \end{array}$

$\begin{array}{l}0.1x+0.2y=0.3\hfill \\ \mathrm{-0.3}x+0.5y=1\hfill \end{array}$

$\begin{array}{l}\hfill \\ \begin{array}{l}\mathrm{-0.01}x+0.12y=0.62\hfill \\ 0.15x+0.20y=0.52\hfill \end{array}\hfill \end{array}$

$\begin{array}{l}0.5x+0.3y=4\hfill \\ 0.25x\mathrm{-0.9}y=0.46\hfill \end{array}$

$\begin{array}{l}0.15x+0.27y=0.39\hfill \\ \mathrm{-0.34}x+0.56y=1.8\hfill \end{array}$

$\begin{array}{l}\begin{array}{l}\\ \mathrm{-0.71}x+0.92y=0.13\end{array}\hfill \\ 0.83x+0.05y=2.1\hfill \end{array}$

$\begin{array}{l}x+y=A\\ x-y=B\end{array}$

$\begin{array}{l}x+Ay=1\\ x+By=1\end{array}$

$\begin{array}{l}Ax+y=0\\ Bx+y=1\end{array}$

$\begin{array}{l}Ax+By=C\\ x+y=1\end{array}$

$\begin{array}{l}Ax+By=C\\ Dx+Ey=F\end{array}$

A stuffed animal business has a total cost of production $C=12x+30$ and a revenue function $R=20x.$ Find the break-even point.

A fast-food restaurant has a cost of production $C(x)=11x+120$ and a revenue function $R(x)=5x.$ When does the company start to turn a profit?

A cell phone factory has a cost of production $C(x)=150x+10,000$ and a revenue function $R(x)=200x.$ What is the break-even point?

A musician charges $C(x)=64x+\mathrm{20,000},$ where $x$ is the total number of attendees at the concert. The venue charges $80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

A guitar factory has a cost of production $C(x)=75x+\mathrm{50,000.}$ If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.