Algebra 1 Final Exam Review Flashcards

Questions and Answers

Use the addition method to solve the system of equations: {5x + 2y = 32 and x - 4 = 2y}

(6, 1)

Mr. Frankel bought 7 tickets to a puppet show and spent $43. Which system of equations will determine the number of adult tickets 'a' and child tickets 'c' he bought?

{4a + 9c = 50 and a + c = 7}

{9a + 4c = 43 and a + c = 7} (correct)

{2a + c = 30 and a + c = 7}

{5a + 2c = 40 and a + 2c = 7}

Solve the system for the value of x: {x + y = 0 and 2x - y = -9}

x = -3

Solve the system for value of x. A) {x - y = 1 and x + y = 3} B) {y = 2/3x + 2 and y = -x - 3}

(2, 1) Signup and view all the answers

The length of a rectangle is 8 cm more than four times the width. If the perimeter is 46 cm, what are the dimensions?

3 cm; 20 cm Signup and view all the answers

Use the substitution method to solve the system of equations: {x + 4y = -1 and 2x - y = 7}

(3, -1) Signup and view all the answers

A rental car agency charges $15 per day plus 11 cents per mile. Another agency charges $18 per day plus 8 cents per mile. How many miles must be driven for costs to equal?

100 miles Signup and view all the answers

The sum of the ages of Petra and her mother is 53. Her mother is 11 years more than twice as old as Petra. How old are Petra and her mother?

Petra 14 years old; Mother 39 years old Signup and view all the answers

Solve the system of equations using the elimination method: {3x + 6y = 9 and x - 6y = 11}

(5, -1) Signup and view all the answers

Which system of equations has no solution?

A) {7z + 9y = 5 and -21x - 27y = 14} Signup and view all the answers

Solve the system: {6x + 4y = 10 and 8x + 12y = -20}

(5, -5) Signup and view all the answers

Which choice best describes the solution(s) of the system of equations? {-24x + 8y = 24 and -15x + 12y = -20}

Infinitely Many Solutions Signup and view all the answers

Study Notes

System of Equations and Solutions

Use the addition method to solve the system {5x + 2y = 32, x - 4 = 2y} yielding the solution (6, 1).
System of equations for ticket purchase: Mr. Frankel can model his purchase using {9a + 4c = 43, a + c = 7} where "a" is adult tickets and "c" is child tickets.
Solve for x in the system {x + y = 0, 2x - y = -9} results in x = -3.

Various Solutions for Systems

For the pairs of equations:
- A) {x - y = 1, x + y = 3} results in (2, 1).
- B) {y = 2/3x + 2, y = -x - 3} yields (-3, 0).

Geometry and Real-world Applications

Dimensions of a rectangle where the length is 8 cm more than four times the width, and perimeter is 46 cm: width is 3 cm, length is 20 cm.
Using substitution method on {x + 4y = -1, 2x - y = 7} results in the solution (3, -1).
Rental car cost comparison: The first agency costs $15 per day plus $0.11 per mile, while the second costs $18 per day plus $0.08 per mile. They equalize at 100 miles.

Age Problems

The sum of Petra and her mother’s ages is 53. Her mother is 11 years older than twice Petra's age, yielding Petra at 14 years and her mother at 39 years.

Elimination Method

Employing the elimination method on {3x + 6y = 9, x - 6y = 11} results in the solution (5, -1).

No Solutions and Multiple Solutions

The system {7z + 9y = 5, -21x - 27y = 14} does not have a solution, indicating inconsistencies between the equations.
For {6x + 4y = 10, 8x + 12y = -20}, the solution is (5, -5).
The system of equations {-24x + 8y = 24, -15x + 12y = -20} has infinitely many solutions, indicating that the lines represented by these equations coincide.

Description

This quiz contains flashcards designed to help you review key concepts for the Algebra 1 final exam. It focuses on methods for solving systems of equations, including the addition method and practical applications like ticket pricing problems. Test your understanding and prepare efficiently for your exam!