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# Five Problems: Addition Method, Linear and Compound Inequality, Absolute Value

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Set 5
#22
2x = 2 - y
3x + y = -1

#26
Solve each by addition method. Determine whether the equations are independent, dependent or inconsistent
X - y = 3
-6x + 6y = 17

#30
-3x + 2y = 8
3x + 2y = 8

#36
Equations involving fractions or decimals. Solve each system by the addition method
3/7x + 5/9y = 27
1/9x + 2/7y = 7

#70
Pennies and nickels. Wendy has 52 coins consisting of nickels and pennies. If the value of the coins is \$1.20 then how many of each type does she have?

#10
Graphing linear inequalities. Graph each linear inequality
y? -3 + 4
#20 x<0

#46
Graphing Compound Inequalities. Determine which of the ordered pairs (1,3), (-2,5), (-6, -4) and (7, -8) satisfy each compound or absolute value inequality
Y ?x -5 or
y? -2x + 1

#68
Absolute Value inequalities. Graph the absolute value inequalities.
|x + 2y| ?6

#98 Applications
Allocating resources. A furniture maker has a shop that can employ 12 workers for 40 hours per week at its maximum capacity. The shop makes tables and chairs. It takes 16 hours of labor to make a table and 8 hours of labor to make a chair. Graph the region that shows the possibilities for the number of tables and chairs that could be made in one week.

See attachment for correct figures.

##### Solution Summary

The addition methods, linear and compound inequalities for absolute values are examined.

##### Solution Preview

Set 5
2x = 2 - y .........................(1)
3x + y = -1 ......................(2)
Solution. We rewrite the 2nd equation as -1=3x+y. Then add it on to the 1st equation. So,
2x-1=(2-y)+(3x+y)
i.e., 2x-1=3x+2
So, x=-3
Then by (2), we have
y=-1-3x=-1-3(-3)=8
So, x=-3, y=8

#26 Solve each by addition method. Determine whether the equations are independent, dependent or inconsistent
x - y = 3 ...........................................(1)
-6x + 6y = 17 ...............................................(2)
Solution. (1)*6 + (2) 
6(x-y)+(-6x+6y)=3*6+17
i.e., 0=35, a ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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