# 2nd 9 Weeks / 6 Weeks Exam Review

Practice | 11 questions (11 autogradable) | 11 points

1.

Last year Mr. Gomez took his family to watch 'The Last Jedi'. He had to buy 2 adult tickets and 1 child ticket for the movie, he paid a total of $41. His brother accompanied him and Mr. Gomez's brother had to buy 2 adult tickets and 2 child tickets, he paid a total of $52. How much does an adult ticket cost, x, and how much does a child ticket cost, y?

Answer should be as a point (x,y)

2.

What is the solution for the following system?

$x\ -\ 3y\ <\ -6\newline2x\ +\ 3y\ \geq\ -3$

(-3, 1)

(0, -1)

(0, 2)

(-2, 2)

3.

Given the system of equations:

$x\ +\ y\ =\ -7\newline x\ -\ 10y\ =\ 4$

What is the value of x?

4.

Solve the system of linear equations:

$3x\ +\ 6y\ -\ 2z\ =\ -6\newline2x\ +\ y\ +\ 4z\ =\ 19\newline-5x\ -\ 2y\ +\ 8z\ =\ 62$

Which set of points represents the solution? (x, y, z)

(-4, 3, 6)

(-1, -3, 6)

(0, 0, 3)

(4, -2, 3)

5.

A father is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63 years. Which of the following best represents the given information?

$f\ =\ 3s\ -\ 3\newline f\ +\ s\ +\ d\ =\ 63\newline s\ =\ d\ -\ 3$

$f\ =\ 3s\newline d\ =\ s\ -\ 3\newline f\ +\ s\ +\ d\ +\ 3\ =\ 63$

$f\ =\ 3s\newline d\ =\ s\ -\ 3\newline(f\ +\ s\ +\ d)\ -\ 3\ =\ 63$

$3f\ =\ s\newline s\ =\ d\ -\ 3\newline(f\ +\ s\ +\ d)\ +\ 3\ =\ 63$

6.

Which of the following describes a system that is **consistent and independent**?

the system has an infinite number of solutions

the system has no solutions

the systems has one solution

the system is broken

7.

Ivan works at Cane's and makes $12 an hour. He only works on the weekend because of sports.

- Ivan would like to make at least $100 each weekend
- Ivan can work more on Sunday than on Saturday
- Ivan's parents only want him to work no more than 15 hours a weekend.

Which system of inequalities best represents the number of hours Ivan can work at Canes on Saturday, x, and on Sunday, y?

$x\ +\ y\ \geq\ 15\newline12x\ +\ 12y\ \leq\ 100\newline x\ <\ y$

$x\ +\ y\ \leq\ 15\newline12x\ +\ 12y\ \leq100\newline x\ <\ y$

$x\ +\ y\ \leq\ 15\newline12(x\ +\ y)\ \geq\ 100\newline x\ >\ y$

$x\ +\ y\ \leq\ 15\newline12(x\ +\ y)\ \geq\ 100\newline x\ <\ y$

8.

Which of the following systems of inequalities satisfies the following:

- Includes all of the points in Quadrant 4
- Does not include the points that lie on the x-axis

$x\ \geq\ 0\newline y\ <\ 0$

$x\ \leq\ 0\newline y\ >\ 0$

$x\ \geq\ 0\newline y\ >\ 0$

$x\ \leq\ 0\newline y\ <\ 0$

9.

Which of the following answers is not a solution of the given system

$3x\ -\ y\ <\ 12\newline-x\ <\ -2y\ +\ 4\newline y\ +\ x\ \geq\ -6$

(0, 0) and (2, 2)

(2, -2) and (-2, -2)

(0, 2) and (2, -6)

10.

On Saturday, 120 people went to a polling location in El Paso. The polling location reported that there were 22 more females than three times the number of males to vote. Which system of equations represents the number of male and female voters that went to the polling location?

$m\ +\ f\ =\ 120\newline f\ =\ 3m\ +\ 22$

$m\ +\ f\ =\ 120\newline f\ +\ 3m\ =\ 22$

$m\ +\ f\ =\ 120\newline f\ +\ 22\ =\ m$

$m\ +\ f\ =\ 120\newline f\ +\ 22\ =\ 3m$

11.

Which of the following satisfies the given system of linear inequalities

$6x\ +\ y\ \leq\ -6\newline x\ +\ 4y\ \leq\ 4\newline y\ >\ -3$

(-4, 4)

(-4, -4)

(0, 0)

(-4, -2)