Q: Which of the following systems has no solution?

$\begin{cases} x + y = 2 \\ x + y = 5 \end{cases}$

Q: Which of the following systems represents a dependent system?

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

Q: A system of inequalities is given by: $\begin{cases} x - 3y < 6 \\ 2x + 3y \geq -6 \end{cases}$ Which region represents the solution set?

The region where the shaded areas of both inequalities overlap.

Q: Which of the following best describes the solution set for the system: $\begin{cases} x^2 + y^2 < 4 \\ y - x^2 \geq 0 \end{cases}$

The region inside the circle and above the parabola.

Q: Which of the following is NOT a step in solving a system of linear equations in three variables by elimination?

Graph the three equations on a number line.

Q: Which of the following best describes the graph of $x < -3$?

A dashed vertical line at $x = -3$ with shading to the left.

Question 1

Which of the following best describes a consistent system of two linear equations in two variables?

Accepted Answer

A system with at least one solution; the lines intersect at one or infinitely many points.

Question 2

Given the system: 
$\begin{cases} 2x - 3y = 4 \ 2x + y = 4 \end{cases}$
Is the ordered pair $(1, 2)$ a solution to the system?

Accepted Answer

No, because it does not satisfy either equation.

Question 3

Solve the following system by substitution:
$\begin{cases} 3x + 2y = 4 \ 2x + y = 1 \end{cases}$

Accepted Answer

$(2, -1)$

Question 4

A company manufactures running shoes with a fixed cost of $300,000 and a variable cost of $30$ per pair. Each pair sells for $80$. What is the break-even point (number of pairs sold)?

Accepted Answer

$6,000$

Question 5

Which of the following systems has no solution?

Accepted Answer

$\begin{cases} x + y = 2 \ x + y = 5 \end{cases}$

Question 6

Solve the following system by the addition method:
$\begin{cases} 4x + 5y = 3 \ 2x - 3y = 7 \end{cases}$

Question 7

Which of the following ordered triples is a solution to the system:
$\begin{cases} x - 2y + 3z = 22 \ 2x - y - z = 5 \ 3x - 5y + 5z = 32 \end{cases}$?

Accepted Answer

$(-1, -4, 5)$

Question 8

Solve the nonlinear system:
$\begin{cases} x^2 + y^2 = 49 \ y^2 - 6x = 49 \end{cases}$

Accepted Answer

$(7, 0)$ and $(0, -7)$

Question 9

Which of the following best describes the graph of the solution set for the inequality $4x - 2y \geq 8$?

Accepted Answer

A solid line with shading to the right of the line.

Question 10

Let $x$ and $y$ be two numbers such that $x + y = 16$ and $xy = 63$. What are the numbers?

Accepted Answer

$7$ and $9$

Question 11

Which of the following is the correct first step to solve the system by substitution?
$\begin{cases} 2x + y = 1 \ 3x + 2y = 4 \end{cases}$

Accepted Answer

Solve the first equation for $y$ in terms of $x$.

Question 12

Which of the following systems represents a dependent system?

Accepted Answer

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

Question 13

A system of inequalities is given by:
$\begin{cases} x - 3y < 6 \ 2x + 3y \geq -6 \end{cases}$
Which region represents the solution set?

Accepted Answer

The region where the shaded areas of both inequalities overlap.

Question 14

Solve the following system of three equations:
$\begin{cases} x + y = -4 \ y - z = 1 \ 2x + y + 3z = -21 \end{cases}$

Accepted Answer

$(-3, -1, -2)$

Question 15

Which of the following best describes the solution set for the system:
$\begin{cases} x^2 + y^2 < 4 \ y - x^2 \geq 0 \end{cases}$

Accepted Answer

The region inside the circle and above the parabola.

Question 16

Which of the following is NOT a step in solving a system of linear equations in three variables by elimination?

Accepted Answer

Graph the three equations on a number line.

Question 17

Given the system:
$\begin{cases} x + y = 1 \ (x-1)^2 + (y+2)^2 = 10 \end{cases}$
What are the solutions?

Accepted Answer

$(2, -1)$ and $(-1, 2)$

Question 18

Which of the following best describes the graph of $x < -3$?

Accepted Answer

A dashed vertical line at $x = -3$ with shading to the left.

Systems of Equations and Inequalities: Study Notes for Precalculus

Study Guide - Practice Questions

Study Guide - Flashcards