1. solve the system by graphing.
{ -2x = 2y - 4
{ 2x - y = -5

2. without graphing, is the system independent, dependent, inconsistent?
{ y = 2x - 8
{ 2x - y = 8

a. dependent
b. independent
c. inconsistent

3. what is the solution of the following system?
{ -2x - y = 1
{ -4x - 2y = -1

a. infinitely many solutions
b. no solution
c. (3,8)
d. (-3,-8)

4. solve the system of inequalities by graphing.
{ y is less than or equal to -4x - 1
{ y > 3x - 1

5. your club is baking strawberry and apple pies for a bake sale. they need at most 18 pies, and cannot have more than 12 apple pies. write and graph a system of inequalities to model this system.

a. let x = the number of strawberry pies. let y = the number of apples pies
{ x is more than or equal to 0
{ y is more than or equal to 0
{ x + y is more than or equal to 18
{ y is less than or equal to 12

b. { x is more than or equal to 0
{ y is more than or equal to 0
{ x + y is less than or equal to 18
{ y is less than or equal to 12

c. { x is more than or equal to 0
{ y is more than or equal to 0
{ x + y is less than or equal to 18
{ y is more than or equal to 12

d. { x is more than or equal to 0
{ y is more than or equal to 0
{ x + y is more than or equal to 18
{ y is more than or equal to 12

6. a rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
using a graphing calculator, to find the number of days for which the costs are the same. round your answer to the nearest whole day.

7. solve the system by substitution.
{ -4.5x - 2y = -12.5
{ 3.25x - y = -0.75

8. solve the system using elimination.
{ 5x + 4y = 12
{ 3x - 3y = 18

9. the length of a rectangle is 9.7 cm more than 4 times the width. if the perimeter of the rectangle is 91.4 cm, what are it's dimensions?

Part 1) Solve the system by graphing.

we have

using a graph tool

see the attached figure N 1

the solution is the point

therefore

the answer part 1) is

Part 2) Without graphing, is the system independent, dependent, inconsistent? -------> equation

-------> equation

Multiply equation by

------->

so

equation is equal to equation

therefore

The system has no solution, is a inconsistent system

the answer part 2) is the option

C. Inconsistent

Part 3) What is the solution of the following system?  

the lines are parallel

so

The system has an infinite number of solutions, it is dependent

therefore

the answer Part 3) is the option

A. Infinitely many solutions

Part 4) Solve the system of inequalities by graphing.  

using a graph tool

see the attached figure N 2

The solution is the shaded area

therefore

the answer part 4) in the attached figure N 2  

Part 5) Your club is baking strawberry and apple pies for a bake sale. They need at most 18 pies, and cannot have more than 12 apple pies. Write and graph a system of inequalities to model this system    

Let  

x -------> the number of strawberry pies

y -------> the number of apples pies

we know that

using a graph tool

see the attached figure N 3

the solution is the shaded area

therefore

the answer Part 5) is the option

B. { x is more than or equal to 0  

{ y is more than or equal to 0  

{ x + y is less than or equal to 18  

{ y is less than or equal to 12

Part 6) A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.  

Using a graphing calculator, to find the number of days for which the costs are the same. Round your answer to the nearest whole day

Let

x-------> the number of days

y-------> total cost to rent a car

we know that

First agency

--------> equation

Second agency

--------> equation

so

to find the number of days for which the costs are the same solve the system of equations

the intersection both graphs is the solution

using a graph tool

see the attached figure N 4

the solution is the point

therefore

the answer is

Part 7) Solve the system by substitution.  

--------> equation

 --------> equation

Substitute equation in equation

find the value of y

therefore

the answer part 7) is

the solution is the point

Part 8) Solve the system using elimination.  

------> equation

------> equation

Multiply equation by

 ------> equation

Multiply equation by

------> equation

Add equation and equation

Find the value of y

therefore

the answer Part 8) is

the solution is the point

Part 9) The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are it's dimensions?

Let

x-------> the length of the rectangle

y-------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

so

Divide by both sides

-------> equation

-------> equation

substitute equation in equation

find the value of x

therefore

the answer part 9) is

the length of the rectangle is

the width of the rectangle is

the answer to the expression is 83

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%