Questions:
Solving and Graphing Systems of Equations
Solve each of the following systems by graphing each of the following.
1. 2x - y = 4
2x - y = 6
2. x-2y = 8
3x - 2y = 12
3. 3x - 6y = 9
X - 2y = 3
4. 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
Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent.
5. 2x + 3y=1
5x + 3y = 16
6. x + 5y = 10
-2x - 10y = -20
7. Solve each of the following problems. Be sure to show the equations used for the solution.
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?
8. 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?
Solve each of the following systems by substitution
9. 5x - 2y = -5
Y - 5x = 3
10. 8x - 4y = 16
Y= 2x - 4
11. 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.
12. 10x + 2y = 7
Y= -5x + 3
Solve each of the following problems. Be sure to show the equation used for the solution.
13. Business and finance. A washer-dryer combination costs $1200. If the washer costs $220 more than the dryer, what does each appliance cost separately?
14. 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.
Solve each of the following systems of linear inequalities graphically.
15. 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.