# Equations and inequalities

Solve the system by the substitution method

6x+5y=10

-4x+y=28

Solve the system by the elimination method

5x+5y=-11

7x-3y= 19

Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

3x-9y=63

2x-6y= -8

What is the solution of the system of equations? ____________________

(Type an ordered pair. Type N if there is no solution. Type R if the solution is all real number.)

Is the system consistent or inconsistent?

A.)___________inconsistent

B.)____________consistent

Are the equation dependent or independent

A) Dependent_______________

B) independent_______

The perimeter of a rectangle is 128 m. The length is 4m more than twice the width. Find the dimensions.

What is the length?

____________m (Simplify your answer)

What is the width?

____________m (Simplify your answer)

Solve.

9/10 (3+6x)+1 >16

x|x| _| _|

Solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.

7x+y=29

8x-9y= -14

What is the solution of the system of equations? ____________________

(Type an ordered pair. Type N if there is no solution. Type R if the solution is all real number.)

Is the system consistent or inconsistent?

A.)___________inconsistent

B.)____________consistent

Are the equation dependent or independent

A) Dependent_______________

B) independent_______

Solve. Then graph

a+9<-122:39 PM 9/28/2008

{a|a< _}

Solve.

4y+2y<54

{y|y _ _}

Graph the system of inequalities

X < 2

Y > -2x+3

Solve. Then graph

7-3x>16 and 4x-1>15

**choose the correct solution**

{x|x>4}

{x|-3<x<4}

{x|x<-3}

0

Determine whether the ordered pair is a solution of the inequality

(9,11), 8y-9x>6

Write interval notation for the set

{x|-6<x<6}

Determine whether the given numbers are solutions of the inequality

7,-10,-13,-1

y-8>2y-2

Use set builder notation to describe the complete solution

7[3m-(m+6)]>2(m-5)

{m|m_ _}

Solve by the elimination methods

0.3x-0.2y=4

0.5x+0.3y= 71/23

Graph and write in interval notation

5<x<13

Graph the inequality on a plane

5x+6y<30

The perimeter of a rectangle is 172 inches the length exceeds the width by 42 inches. Find the length and the width.

____________m (Simplify your answer)

What is the width?

____________m (Simplify your answer)

Miguel's insurance company will replace his car if repair costs exceed 80% of the car's value the car recently sustained $5600 worth of damage but it was not replaced. What was the value of his car

What was the value of his car?

One canned juice drink is 25% orange juice, another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice?

How many liters of the 25% orange juice should be in the mixture _ L

How many liters of the 10% orange juice should be in the mixture _ L

A cellular phone company offers a contract for which the cost C in dollars, of t minutes of telephoning is given by C=0.25(t-500)+75.95, where it is assumed that t³500 minutes. What times will keep costs between $122.70 and $158.45.

For the cost to be between 122.70 and 158.45, the telephoning time must be between _ min. and _ min.

Classify the graph of the system as consistent or inconsistent and as dependent or independent. Then match it with the correct system.

Is the system consistent or inconsistent?

A.)___________inconsistent

B.)____________consistent

Are the equation dependent or independent

A) Dependent_______________

B) independent_______

a) x=4,y=-8

b) y=4x, y=-8x

c) x=-8, y=4

Solution (4,-8)

#### Solution Preview

Please see the attached file for all my answers for the question up to

"Solve by the elimination methods

0.3x - 0.2y = 4

0.5x + 0.3y = 71/23"

I am sorry that I am encountering a technical difficulty in Microsoft word. Here are my responses for the rest of the questions.

Question: "Graph and write in interval notation 5<13"

Answer:

Since the inequality is always true, the solution is {x | x E R} (or all x that belongs to all real numbers)

The graph of the solution is a horizontal line representing the x-axis and darken the entire line to represent the solution set.

Question: "Graph the inequality on a plane 5x + 6y < 30"

Answer:

Graph the line 5x + 6y = 30 with x-intercept (6, 0) and y-intercept (0, 5)

This is a line pointing down from ...

#### Solution Summary

This provides several examples of solving systems of equations and inequalities, including word problems and graphing.