# Solving and graphing inequalities and system of equations

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Math

Here are some more problems I would like help with.

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

6x-6y= -12

6y-6x= 12

What is the solution of the system of equations?

a) A point

b) Infinitely many solutions

c) No solution

Is the system consistent or inconsistent?

3. Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and Train B is traveling a 64 mph. Train A passes a station at 11:20 PM If train B passes the same station at 11:50 PM at what time will Train B catch up to Train A?

When will train B catch up with train A?

4. Decide whether the pair of lines is parallel, perpendicular, or neither.

5x+4y=9

4x+5y=5

The lines are A) perpendicular B) neither C) parallel

5.) Collect like terms.

14x+5y-6x-8y

6.) Find the indicated outputs for f(x)=4x to 2 power -2x

f(0)=________

f (-1)=______

f(2)=_______

7.) Solve

8x-(4x+8)=8

The solution is x=_________

9.) 50% of what number is 30?

Answer is __________

10.)

Determine whether (9,6) is a solution of 5x+6y=1

Is (9,6) a solution to the equation?

Yes__________ No____________

11.) Find the slope and the y-intercept.

F(x) = -5x-6

The slope is __________

The y-intercept is [0, ____]

12.) Solve using the addition and multiplication principles.

4+7x<11

The solution set is {x|x ___ ____}

(

(Type an inequality symbol, then type an integer or a fraction)

13.) On three consecutive passes, a football team gains 9 yards, loses 18 yards, and gains 50 yards. What number represents the total net yardage?

The total net yardage is _______yards?

14.) Use the distributive property to help you solve the equation?

9 (w-2) = 18

w=________

16.) Solve

x + x = + x

The solution is x=_________

( simplify your answer. Type an integer or a fraction)

19.) In 1992, the life expectancy of males in a certain country was 65.9 years. In 1996, it was 68.4 years. Let E represent the life expectancy in years t and let t represent the number of years since 1992.

The linear function E (t) that fits the data is

E (t)= _____ t + _______.

(round to the nearest tenth)

Use the function to predict the life expectancy of males in 2008.

E (16) = ?

(Round to the nearest tenth.)

20. Translate to an algebraic expression.

The product of 32% and some number

The translation is _?

(type the percentage as a decimal. Use q to represent some number.)

21.) Solve for the indicated letter.

d= 9e, for e

The solution is e = ?

22.) Solve using the multiplication principle. Don't forget to perform a check.

- x = -

The solution is _?

(simplify your answer. Type an integer or a fraction)

25.) Solve. Then do line graph.

6x 30

Choose the correct solution.

A. {x|x

B. {x|x>5}

C. {x|x

D. {x|x<5}

27.) Find the slope, if it exists.

x = -5

m=________

(Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.)

28.) Find the domain of the function.

g (x) =

Choose the correct domain below.

A.) { x| x 0}

B.)

C.) {x |x }

D.) {x |x }

30.) Find the domain of the function.

p(x) = x to the 2nd power -2x +4

What is the domain of p?

A) {x|x

B) {x|x is a real number}

C) {x|x>0}

D) {x|x 4}

31.) Solve by the elimination method.

5x+6y=4

10x+12y=8

What is the solution of the system?

(Type an ordered pair. Type an integer or a fraction. Type N if there is no solution. Type I if there are in infinitely many solution)

32.) Amy paid $87.81 for a pair of running shoes during a 30% off sale. What was the regular price?

The regular price was $ _______.

(Round to the nearest cent, if necessary)

33.) The equation y= -1777x+27,153 can be used to predict the number y of gun deaths in the United States x years after 2000, that is, x=0 corresponds to 2000,x=3 corresponds to 2003, x=6 corresponds to 2006, and so on. Predict the number of gun deaths in 2006 and 2007. In what year will the number of gun deaths be 11,160?

The predicted gun death in 2006 will be _________2007_______

The predicted number of gun deaths will be 11,160 in the year _______.

37.) Solve by the substitution method.

8x+3y= -6

x=9-2y

What is the solution of the system?

(Type an ordered pair. Type N if there is no solution)

38.) Simplify

-2[46-(41-95)]=________

39.) Solve the following system of equations.

x+2y= (1)

x=4-2y (2)

What is the solution of the system? ___________

(Type an ordered pair. Type N if there is no solution)

40.) Find the slope, if it exists, of the line containing the pair of points.

(8,3) and (9,-1)

The slope m = ________

(Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined)

41.) The function H described by H (x) = 2.75x + 71.48 can be used to predict the height, in centimeters, of a woman whose humerus (bone from the elbow to the shoulder) is x cm long.

Predict the height of a woman whose humerus is 35 cm long.

The predicted height of a woman whose is 35 cm long is ____cm.

42._ Solve

0.8x+1

The solution is {x|x ____ ____}

(Simplify your answer. Type an inequality symbol; then type and integer or a decimal.)

43) Solve using the multiplication principle.

-7x>

The solution set is {x|x ____ _____}

(Type an inequality symbol and a fraction)

44. Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 12% protein?

How many pounds of the cornmeal should be in the mixture?

______----pounds

How many pounds of the soybean meal should be in the mixture?

________ pounds

45.) The width of a rectangle is fixed at 22 cm. What length will make the perimeter greater than 96 cm?

The length must be greater than ________cm

48.) Solve

-0.2x<-16

The solution is {x| _____}

50.) Solve

-22

The solution is {x| ___ __}

( Type an integer or a fraction)

51.) Solve

5>-4x+4 or 9

Choose the solution to the inequality.

A. (-

B. [- - ] [- , ]

C. [- ,- ]

D. [- , ]

52.) Multiply

,[ ] = _______

(Type an integer or a simplified fraction)

53.) Evaluate

for a = 39 and b = 1

= _________

(Simplify your answer)

#### Solution Summary

It includes detailed solutions to several problems on solving and graphing inequalities and system of equations/inequalities.