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
8.2 Exercises - Systems of Linear Equations:
Solving by Adding
1. Solve systems of linear equations using the addition method
2. Solve applications of systems of linear equations
The graphical method of solving equations, shown in Section 8.1, has two definite disadvantages. First, it is time-consuming to graph each system that you want to solve. More importantly, the graphical method is not precise. For instance, look at the graph of the system. 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. Jill has $3.50 in nickels and dimes. Of she has 50 coins, how many of each type of coin does she have?
60. 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?
8.3 Exercises - Systems of Linear Equations:
Solving by Substitution
1. Solve systems using the substitution method
2. Choose an appropriate method for solving
2. 3. Solve applications of systems of equations
16. 5x - 2y = -5
Y - 5x = 3
20. 8x - 4y = -16
y = 2x - 4
28. 4x - 12y = 5
-x + 3y = -1
38. 10x + 2y = 7
y = -5x + 3
56. 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. 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.
8.4 Systems of Linear Inequalities
1. Graph a system of linear inequalities
2. Solve an application of linear inequalities
Our previous work in this chapter dealt with finding the solution set of a system of linear equations. That solution set represented the points of intersection of the graphs of the equations in the system. In this section, we extend that idea to include systems of linear inequalities. In this case, the solution set for each inequality is all ordered pairs that satisfy that inequality.
The graph of the solution set of a system of linear inequalities is then the intersection of the graphs of the individual inequalities.
The solution elaborates the methods of solving system of linear equations and inequalities, such as addition, subtraction, substitution, and graphing. Supplemented with graphs and step-by-step detailed explanations, the solution provides the student a guide on how to solving the system of linear equations and inequalities.