연립일차방정식

For the following exercises, solve each system in terms of $A,B,C,D,E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD.$

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

For the following exercises, solve each system in terms of $A,B,C,D,E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD.$

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

For the following exercises, solve each system in terms of $A,B,C,D,E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD.$

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

For the following exercises, solve each system in terms of $A,B,C,D,E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD.$

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

For the following exercises, solve each system in terms of $A,B,C,D,E,$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD.$

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

For the following exercises, solve for the desired quantity.

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

For the following exercises, solve for the desired quantity.

An Ethiopian 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?

For the following exercises, solve for the desired quantity.

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?

For the following exercises, solve for the desired quantity.

A musician charges $C(x)=64x+20,000$ 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?

For the following exercises, solve for the desired quantity.

A guitar factory has a cost of production $C(x)=75x+50,000.$ 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.

For the following exercises, use a system of linear equations with two variables and two equations to solve.

Find two numbers whose sum is 28 and difference is 13.

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.

For the following exercises, use a system of linear equations with two variables and two equations to solve.

The startup cost for a restaurant is $120,000, and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi service would charge $20 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A total of 1,595 first- and second-year college students gathered at a pep rally. The number of first-years exceeded the number of second-years by 15. How many students from each year group were in attendance?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

276 students enrolled in an introductory chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.

For the following exercises, use a system of linear equations with two variables and two equations to solve.

There were 130 faculty at a conference. If there were 18 more women than men attending, how many of each gender attended the conference?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

A jeep and a pickup truck enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the pickup did, and traveled 7 mph slower than the pickup. After 2 hours from the time the pickup entered the highway, the cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control and retained the same speed.

For the following exercises, use a system of linear equations with two variables and two equations to solve.

If a scientist mixed 10% saline solution with 60% saline solution to get 25 gallons of 40% saline solution, how many gallons of 10% and 60% solutions were mixed?

For the following exercises, use a system of linear equations with two variables and two equations to solve.

An investor earned triple the profits of what they earned last year. If they made $500,000.48 total for both years, how much did the investor earn in profits each year?