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# em of linear equations and compound inequality

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1. Solve each system by graphing.
y = - 2/3 x
2x + 3y = 5

2. Solve each system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.

2x - y = 4
2x - y = 3

3. Write a system of two equations in two unknowns for each problem. Solve each system by substation.

4. Investing her bonus. Donna invested her \$33,000 bonus and received a total of \$970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?

5. Solve each system by the addition method
a) x + y = 13
22x + 36y = 356

b) 3x + 5y = 27
7 9

c) 1x + 2y = 7
8 7

6. Determine whether - 4 satisfies each compound inequality
3x > 0 and 3x - 4 < 11

7. Graph the solution set to each compound inequality
x > 3 or x < - 3

8. Two test only. Professor Davis counts his midterm as 2/3 of the grade. And his final as 1/3 of the grade. Jason scored only 64 on the midterm. What range of scores on the final exam would put Jason's average between 70 and 79 inclusive?

9. Solve each absolute value equation
| 3 - 3x | = 1
4 4

10. Solve each absolute value inequality and graph the solution set.
1 |
3 | 2x -1 | < 1

11. Graph each compound inequality
x > - 2y and
x - 3y < 6

12. Graph the absolute value inequalities
| x + 2y | > 6

13. A study by Dr. Aaron R Folsom concluded that waist-to-hip rations are a better predictor of 5-year survival than more traditional height to weight ratios. Dr. Folsom concluded that for good health the waist size of a woman aged 50 to 69 should be less than or equal to 80% of her hip size, w < 0.80h. Make a graph showing possible waist and hip sizes for good health for women in this age group for which hip size is no more than 50 inches.