Question 1

Given the system of equations:

$$\begin{align*}
-15x + 9y &= 15 \
3x - y &= 0
\end{align*}$$

Which graph below best represents the solution to this system?

Accepted Answer

Graph A

Question 2

A company sells exercise DVDs for $$19.95 each. The monthly fixed costs are 20$$,520 and the variable cost per DVD is $$6.65. What is the cost equation C$ in terms of x$, the number of DVDs produced?

Accepted Answer

$$C = 20,520 + 6.65x$$

Question 3

Given the system:

$$\begin{align*}
-2x - 3y &= 4 \
4x + 6y &= -8
\end{align*}$$

Which graph below best represents the system?

Accepted Answer

Graph C

Question 4

Solve the system by the addition method:

$$\begin{align*}
4x + 15y &= 16 \
4x - 15y &= 16
\end{align*}$$

What is the solution?

Accepted Answer

Question 5

Solve the system using substitution or elimination:

$$\begin{align*}
9x - 4y &= 6 \
-18x + 8y &= -11
\end{align*}$$

What is the solution?

Accepted Answer

There is no solution.

Question 6

Solve the system of equations using substitution or elimination:

$$\begin{align*}
2x + 7y &= -4 \
2x + 3y &= 4
\end{align*}$$

What is the solution?

Accepted Answer

$$( -2, 2 )$$

Question 7

Use a graphing calculator to solve the system:

$$\begin{align*}
y &= 2x - 1 \
y &= 10x - 5
\end{align*}$$

What is the solution? (Round to three decimal places as needed.)

Accepted Answer

Question 8

A small plant manufactures riding lawn mowers. The fixed costs are $$44,000 per day and the variable cost per mower is 1$$,500. Each mower sells for $$2,000. What is the cost equation C$ in terms of x$, the number of mowers produced?

Accepted Answer

$$C = 44,000 + 1,500x$$

Question 9

For the lawn mower company, what is the revenue equation $$R in $$terms of $$x$$?

Accepted Answer

$$R = 2,000x$$

Question 10

How many riding lawn mowers must be manufactured and sold each day for the company to break even? (Use the cost and revenue equations from the previous questions.)

Accepted Answer

$$88$$

Question 11

A company’s cost equation is $$C = 20,520 + 6.65x$$ and its revenue equation is $$R = 19.95x. $$How many DVDs must be sold to break even?

Accepted Answer

$$1,536$$

Question 12

Given the system:

$$\begin{align*}
y &= 2x - 1 \
y &= 10x - 5
\end{align*}$$

What is the $$x-$$coordinate of the intersection point?

Accepted Answer

$$0.5$$

Question 13

If a system of equations has no solution, what does this mean about the graphs of the equations?

Accepted Answer

The lines are parallel and never intersect.

Question 14

If a system of equations has infinitely many solutions, what does this mean about the equations?

Accepted Answer

The equations represent the same line.

Question 15

A company’s cost equation is $$C = 20,520 + 6.65x$$ and its revenue equation is $$R = 19.95x. $$What is the profit equation $$P in $$terms of $$x$$?

Accepted Answer

$$P = 19.95x - (20,520 + 6.65x)$$

College Algebra Study Guide: Systems of Equations and Applications

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