Question 1

Which of the following best describes a system of equations that has exactly one solution?

Accepted Answer

The lines intersect at a single point.

Question 2

Given the system of equations:

$$4x - y = 9$$

$$6x + 3y = 15$$

What is the solution to this system?

Accepted Answer

$$(1.5, 2)$$

Question 3

A concert promoter needs to make $$84,000 from the sale of 2400 tickets. Tickets cost 30 $$and $$45. If x$ is the number of 30 $$tickets$$ and y$ is the number of 45 $$tickets$, which system of equations models this scenario?

Accepted Answer

$$x + y = 2400$$ and $$30x + 45y = 84,000$$

Question 4

If the revenue function is $$R(x) = 23.50x + 1192.50$$ and the cost function is $$C(x) = 20x$$, what is the break-even point?

Accepted Answer

$$x = 18$$

Question 5

Solve the inequality $$3(x - 4) \leq 7x - 13$$ and give the solution in interval notation.

Accepted Answer

$$(-\infty, \frac{5}{2}]$$

Question 6

Which method involves solving one equation for one variable and substituting into the other equation?

Accepted Answer

Substitution

Question 7

Given the system:

$$2x + 2y = 4$$

$$x + y = 2$$

What type of solution does this system have?

Accepted Answer

Infinitely many solutions

Question 8

Market equilibrium occurs when supply quantity equals demand quantity. If $$P = 50.50 + 0.80q$$ and $$P = 400 - 0.70q$$, what is the equilibrium price $$P$$?

Accepted Answer

$$P = 236.90$$

Question 9

Which of the following systems is inconsistent?

Accepted Answer

$$y = 2x + 4$$ and $$y = 2x - 5$$

Question 10

Solve the compound inequality $$-6 \u003c 3x + 6 \u003c 6$$ and express the solution in interval notation.

Accepted Answer

$$[-4, 3]$$

Question 11

If a system of equations is dependent, what does this mean about the graphs of the equations?

Accepted Answer

The lines coincide and have infinitely many solutions.

Question 12

A promoter sells $$x$$ tickets at $$30 each$$ and $$y$$ tickets at $$45 each to $$make $$84,000$$ from $$2400$$ tickets. How many $$45 tickets$$ were sold?

Accepted Answer

$$y = 1600$$

Question 13

Which of the following is the correct interval notation for the solution to $$2x + 2 \leq 14 or$$ $$x - 8 \geq 0$$?

Accepted Answer

$$(-\infty, 6] \cup [8, \infty)$$

Question 14

Which of the following is NOT a method for solving a system of linear equations?

Accepted Answer

Quadratic Formula

Question 15

If $$f(x) = x^2$ and g(x) = x + 3$, for which x$ does f(x) = g(x$$)$$?

Accepted Answer

$$x = -1$$ and $$x = 3$$

Question 16

Which scenario best represents a system with no solution?

Accepted Answer

Two lines that are parallel and have different $$y-$$intercepts.

Question 17

If $$f(x) \u003e g(x)$$, which region on the graph represents the solution?

Accepted Answer

Where the graph of $$f(x) is $$above $$g(x).$$

Question 18

Which of the following is the correct solution to $$9x - 12 \leq 7x - 13$$?

Accepted Answer

$$x \leq \frac{5}{2}$$

Question 19

If a system of equations is solved by elimination and the result is $$0 = 0$$, what does this indicate?

Accepted Answer

The system has infinitely many solutions.

Systems of Equations and Linear Inequalities: Study Notes for College Algebra

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