# Solving a System by Graphing, substitution & elimination

Problem #20

Solving a System by Graphing

Solve each system by graphing.

y = − 2/3x

2x + 3y =5

Problem # 56

Solving by Substitution

Solve each system by substitution. Determine whether the

equations are independent, dependent, or inconsistent.

2x − y = 4

2x − y = 3

Problem # 70

Solve each system by the substitution method.

x + 3y = 2

− x + y = 1

Problem # 92

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?

Problem # 30

Solve each system by the addition method. Determine whether

the equations are independent, dependent, or inconsistent.

− 3x + 2y = 8

3x + 2y = 8

Problem # 52

Solve each system by substitution or addition, whichever is easier.

2y − x = 3

x = 3y − 5

Problem # 72

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?

Problem # 82

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?

#### Solution Summary

Detailed explanations are given.