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

The lines coincide and have infinitely many solutions.

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

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

Q: Which scenario best represents a system with no solution?

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

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 $-6 < 3x + 6 < 6$ 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 $f(x) > g(x)$, 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

Study Guide - Practice Questions

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