Explore BrainMass
Share

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

Set 5
#22
The addition method. Solve each by addition
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.

© BrainMass Inc. brainmass.com July 18, 2018, 3:08 am ad1c9bdddf

Attachments

Solution Preview

Please see the attached file.

Set 5
#22 The addition method. Solve each by addition
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 ...

Solution Summary

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

$2.19