Graphing Systems of Equations

PROBLEMS I NEED HELP WITH

Problems #'s 10, 12, 20, 26 these I need help completing
Hint: (in order to draw points and lines on the graph I use Paint) Click on it and copy/paste it into an open Paint file
1. Click on the spray-paint icon and then choose the smallest splotch (there were three sizes
2. After you plot the points then paste again into word (same applies for a line)

Solve each of the following systems by graphing.

10. 2x - y = 4
2x - y = 6

12. x - 2y = 8
3x - 2y = 12

20. 3x - 6y = 9
x - 2y = 3

26. Find values for m and b in the following system so that the solution to the system is (-3, 4).

5x + 7y = b
mx + y = 22

Next problem #'s 12, 20, 56, 60

Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.

12. 2x + 3y = 1
5x + 3y = 16

20. x + 5y = 10
-2x - 10y = -20

56. Number problems. Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?

60. Business and finance. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?

Next problem #'s 16, 20, 28, 38, 56, 58

Solve each of the following systems by substitution.

16. 5x - 2y = -5
y - 5x = 3

20. 8x - 4y = 16
y = 2x - 4

28. 4x - 12y = 5
-x + 3y = -1

Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.

38. 10x + 2y = 7
Y = -5x + 3

56. Social science. In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?

58. Geometry. The length of a rectangle is 2 in. more than twice its width. If the perimeter of the rectangle is 34 in., find the dimensions of the rectangle.

Last problem #'s 10, 20

Solve each of the following systems of linear inequalities graphically.

10. 3x - y < 6
x > 1
y < 3

20. A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week. The plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. Write a system of inequalities representing this situation. Then, draw a graph of the feasible region given these conditions, in which x is the number of AM radios and y the number of AM/FM radios.