Q: Which of the following systems is inconsistent?

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

Q: A system of equations models the number of adult and child tickets sold for a concert. If $$x is $$the number of adult tickets and $$y is $$the number of child tickets, which system correctly models the scenario: 200 tickets sold, $$x + y = 200$$, and total sales of $$\3700$ with adult tickets at $$\$$25$$ and child tickets at $$\10$?

$$\begin{cases} x + y = 200 \\ 25x + 10y = 3700 \end{cases}$$

Q: Which of the following systems is dependent?

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

Question 1

Which of the following best describes the solution to a system of two linear equations whose graphs are parallel lines?

Accepted Answer

No solution

Question 2

Given the system of equations:

$$\begin{cases} 2x + 3y = 7 \ 4x + 6y = 14 \end{cases}$$

What is the nature of its solution?

Accepted Answer

Infinitely many solutions

Question 3

Which method is most efficient for solving the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

Elimination

Question 4

If the determinant of the coefficient matrix in a system of two equations is zero, what does this imply about the system?

Accepted Answer

The system has no solution or infinitely many solutions

Question 5

Solve the system using Cramer's Rule:

$$\begin{cases} 3x + 2y = 7 \ 2x - y = 4 \end{cases}$$

What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 6

Which of the following systems represents a real-world scenario that can be modeled by a system of equations?

Accepted Answer

Finding the intersection of two roads

Question 7

Given the system:

$$\begin{cases} x^2$ + y^2$ = 25 \ y = x + 1 \end{cases}$$

How many solutions does this system have?

Accepted Answer

Two solutions

Question 8

What is the determinant of the matrix $$\begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix}$$?

Accepted Answer

Question 9

Which of the following is NOT a possible outcome when solving a system of three linear equations in three variables?

Accepted Answer

Exactly two solutions

Question 10

A system of equations is given by:

$$\begin{cases} x + 2y = 10 \ 3x - y = 5 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (3, 3.5)$$

Question 11

Which of the following systems is inconsistent?

Accepted Answer

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

Question 12

Given the system:

$$\begin{cases} x^2$ = y \ x + y = 6 \end{cases}$$

What are the solutions?

Accepted Answer

$$(2, 4)$$ and $$(3, 3)$$

Question 13

Which of the following is the correct formula for the determinant of a $$2 	imes 2$$ matrix $$\begin{pmatrix} a & b \ c & d \end{pmatrix}$$?

Accepted Answer

$$ad - bc$$

Question 14

A system of equations models the number of adult and child tickets sold for a concert. If $$x is $$the number of adult tickets and $$y is $$the number of child tickets, which system correctly models the scenario: 200 tickets sold, $$x + y = 200$$, and total sales of $$\3700$ with adult tickets at $$\$$25$$ and child tickets at $$\10$?

Accepted Answer

$$\begin{cases} x + y = 200 \ 25x + 10y = 3700 \end{cases}$$

Question 15

Which of the following is true about the solution to the system $$\begin{cases} x^2$ + y^2$ = 9 \ y = 2x \end{cases}$$?

Accepted Answer

There are two solutions

Question 16

What is the solution to the system $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 1)$$

Question 17

Which of the following is a valid use of matrices in solving systems of equations?

Accepted Answer

Finding the intersection point of two lines

Question 18

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

Accepted Answer

The graphs are the same line

Question 19

Which of the following systems is dependent?

Accepted Answer

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

Unit 3 Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드