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

 Page 8 / 20

$\begin{array}{c}5x-y=4\text{\hspace{0.17em}}\\ x+6y=2\end{array}$ and $\text{\hspace{0.17em}}\left(4,0\right)$

and $\left(-6,1\right)$

Yes

$\begin{array}{c}3x+7y=1\text{\hspace{0.17em}}\\ 2x+4y=0\end{array}$ and $\text{\hspace{0.17em}}\left(2,3\right)$

and $\left(-1,1\right)$

Yes

$\begin{array}{c}x+8y=43\text{\hspace{0.17em}}\\ 3x-2y=-1\end{array}$ and $\text{\hspace{0.17em}}\left(3,5\right)$

For the following exercises, solve each system by substitution.

$\left(-1,2\right)$

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

$\left(-3,1\right)$

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

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

$\left(-\frac{3}{5},0\right)$

No solutions exist.

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

$\left(\frac{72}{5},\frac{132}{5}\right)$

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

For the following exercises, solve each system by addition.

$\left(6,-6\right)$

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

$\left(-\frac{1}{2},\frac{1}{10}\right)$

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

No solutions exist.

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

$\left(-\frac{1}{5},\frac{2}{3}\right)$

$\left(x,\frac{x+3}{2}\right)$

For the following exercises, solve each system by any method.

$\left(-4,4\right)$

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

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

$\left(\frac{1}{2},\frac{1}{8}\right)$

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

$\left(\frac{1}{6},0\right)$

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

$\left(x,2\left(7x-6\right)\right)$

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

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

$\left(-\frac{5}{6},\frac{4}{3}\right)$

## Graphical

For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions.

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

Consistent with one solution

Consistent with one solution

Dependent with infinitely many solutions

## Technology

For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth.

$\begin{array}{l}\hfill \\ \begin{array}{l}-0.01x+0.12y=0.62\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.15x+0.20y=0.52\hfill \end{array}\hfill \end{array}$

$\left(-3.08,4.91\right)$

$\begin{array}{l}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.5x+0.3y=4\hfill \\ 0.25x-0.9y=0.46\hfill \end{array}$

$\begin{array}{l}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.15x+0.27y=0.39\hfill \\ -0.34x+0.56y=1.8\hfill \end{array}$

$\left(-1.52,2.29\right)$

$\begin{array}{l}\begin{array}{l}\\ -0.71x+0.92y=0.13\end{array}\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.83x+0.05y=2.1\hfill \end{array}$

## Extensions

For the following exercises, solve each system in terms of $\text{\hspace{0.17em}}A,B,C,D,E,\text{}$ and $\text{\hspace{0.17em}}F\text{\hspace{0.17em}}$ where $\text{\hspace{0.17em}}A–F\text{\hspace{0.17em}}$ are nonzero numbers. Note that $\text{\hspace{0.17em}}A\ne B\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}AE\ne BD.$

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

$\left(\frac{A+B}{2},\frac{A-B}{2}\right)$

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

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

$\left(\frac{-1}{A-B},\frac{A}{A-B}\right)$

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

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

$\left(\frac{CE-BF}{BD-AE},\frac{AF-CD}{BD-AE}\right)$

## Real-world applications

For the following exercises, solve for the desired quantity.

A stuffed animal business has a total cost of production $\text{\hspace{0.17em}}C=12x+30\text{\hspace{0.17em}}$ and a revenue function $\text{\hspace{0.17em}}R=20x.\text{\hspace{0.17em}}$ Find the break-even point.

A fast-food restaurant has a cost of production $\text{\hspace{0.17em}}C\left(x\right)=11x+120\text{\hspace{0.17em}}$ and a revenue function $\text{\hspace{0.17em}}R\left(x\right)=5x.\text{\hspace{0.17em}}$ When does the company start to turn a profit?

They never turn a profit.

A cell phone factory has a cost of production $\text{\hspace{0.17em}}C\left(x\right)=150x+10,000\text{\hspace{0.17em}}$ and a revenue function $\text{\hspace{0.17em}}R\left(x\right)=200x.\text{\hspace{0.17em}}$ What is the break-even point?

A musician charges $\text{\hspace{0.17em}}C\left(x\right)=64x+20,000,\text{}$ where $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ 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? $\left(1,250,100,000\right)$ A guitar factory has a cost of production $\text{\hspace{0.17em}}C\left(x\right)=75x+50,000.\text{\hspace{0.17em}}$ 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. #### Questions & Answers (1+cosA)(1-cosA)=sin^2A BINCY Reply good Neha why I'm sending you solved question Mirza Teach me abt the echelon method Khamis exact value of cos(π/3-π/4) Ankit Reply What is differentiation? Intakhab Reply modul questions trigonometry Thamarai Reply (1+cosA)(1-cosA)=sin^2A BINCY differentiate f(t)=1/4t to the power 4 +8 Jessica Reply I need trigonometry,polynomial duru Reply ok Augustine Why is 7 on top Bertha Reply simplify cot x / csc x Catherine Reply 👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay what is the period of cos? SIYAMTHEMBA Reply your question might not seem clear as you asked. ask well to get perfect answers put your question on a table I'm willing to help you Mr Siyamthemba Patrick simplify: cot x/csc x Catherine sorry i didnt realize you were actually asking someone else to put their question on here. i thought this was where i was supposed to. Catherine some to dereve formula for bulky density kurash Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero Rahul Reply questions Thamarai ok AjA sin^4+sin^2=1, prove that tan^2-tan^4+1=0 SAYANTANI Reply what is the formula used for this question? "Jamal wants to save$54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx