Q: Which of the following systems of equations has infinitely many solutions?

$$\begin{cases} 2x + 3y = 6 \\ 4x + 6y = 12 \end{cases}$$

Question 1

Which of the following systems of equations has infinitely many solutions?

Accepted Answer

$$\begin{cases} 2x + 3y = 6 \ 4x + 6y = 12 \end{cases}$$

Question 2

A chemist needs 10 liters of a 30% acid solution. She has only 20% and 50% acid solutions. How many liters of the 50% solution should she use?

Accepted Answer

$$5$$ liters

Question 3

Solve the system using elimination: $$\begin{cases} 4x + 3y = 11 \ 3x - 2y = 5 \end{cases}$$

Accepted Answer

$$(2, 1)$$

Question 4

Which graph represents a system with no solution?

Accepted Answer

Two parallel lines

Question 5

If $$|2x - 5| = 9$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 7, x = -2$$

Question 6

A person invests $$\2000$ in an account earning 3$$\%$$ simple interest and $$\$$3000 in an $$account earning $$5\%$$ simple interest. What is the total interest earned in one year?

Accepted Answer

Question 7

Solve the inequality $$3x - 2 \geq 4. $$Express the solution in interval notation.

Accepted Answer

$$[2, \infty)$$

Question 8

Which of the following best describes the solution set for $$|x - 2| \u003c 4$$?

Accepted Answer

$$(-2, 6)$$

Question 9

A company’s revenue is modeled by $$R = 40x + 10000$$, where $$x is $$the number of units sold. What is the revenue if 300 units are sold?

Accepted Answer

$$\22000$

Question 10

Which of the following is the correct solution to the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(3, 2)$$

Question 11

If $$y = 2x + 1$$ and $$y = -x + 4$$, what is the solution to the system?

Accepted Answer

$$(1, 3)$$

Question 12

A solution to $$|x + 3| = 7 is$$:

Accepted Answer

$$x = 4 or$$ $$x = -10$$

Question 13

Which of the following inequalities is represented by the shaded region above the line $$y = 2x - 1$$?

Accepted Answer

$$y \u003e 2x - 1$$

Question 14

If $$|x - 4| \geq 2$$, what is the solution in interval notation?

Accepted Answer

$$(-\infty, 2] \cup [6, \infty)$$

Question 15

A business has fixed costs of $$\7000$ and variable costs of $$\$$20$$ per unit. Write the total cost function $$C(x).$$

Accepted Answer

$$C(x) = 20x + 7000$$

Question 16

Solve for $$x$$: $$2|x - 3| = 10$$

Accepted Answer

$$x = 8, x = -2$$

Question 17

Which of the following is the solution to $$|x| \u003c 3$$?

Accepted Answer

$$(-3, 3)$$

Question 18

If $$y = 3x - 2$$ and $$y = -x + 6$$, what is the solution to the system?

Accepted Answer

$$(2, 4)$$

Question 19

A person invests $$\4000$ at 4$$\%$$ annual interest and $$\$$6000 at$$ $$5\%$$ annual interest. What is the total interest earned in one year?

Accepted Answer

$$\490$

College Algebra Study Notes: Systems of Linear Equations, Linear Functions, and Inequalities

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