# 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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#### 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.

system of linear equation and compound inequality

Please see attached file for full problem description.

Solve system by the substitution method.

1. y = 2x - 6

y = x - 5

2. 7x - 4y = 26

y = x - 5

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Solve each system by the addition method. If there is no solution or an infinite number of solutions, so state.

3.6x + 2y = 8

2x - y = 6

4. 7x - 2y = 8

-14x + 4y = 8

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5. Solve the compound inequality. Give the graph or describe it.

x < 5 and x > 4

Solve each absolute value equation or inequality

6.|x - 5 | > -1

Solve the inequality:

7. 3 | 2x +3 | + 6 > 0

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