Assignment:
Solving a System by Graphing
Solve each system by graphing.
y = − 2/3x
2x + 3y =5
Q1: Solving by Substitution
Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.
2x − y = 4
2x − y = 3
Q2: Solve each system by the substitution method.
x + 3y = 2
− x + y = 1
Q3: Applications
Write a system of two equations in two unknowns for each problem. Solve each system by substitution.
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?
Q4: Solve each system by the addition method. Determine whether the equations are independent, dependent, or inconsistent.
− 3x + 2y = 8
3x + 2y = 8
Q5: Solve each system by substitution or addition, whichever is easier.
2y − x = 3
x = 3y − 5
Q6: Applications
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice.
Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?
Q7: Applications
Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice.
Super Bowl contender. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?