# 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.

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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.