# Solving systems of equations

1. Solve by substitution or elimination method:

3x - 2y = 8

-12x + 8y = 32

2. Solve by substitution or elimination method:

7x - 5y = 14

-4x + y = 27

3. Solve by substitution or elimination method:

-4x + 3y = 5

12x - 9y = -15

4. A university bookstore recently sold a wire bound graph-paper notebook for $2.50 and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks was sold for a total of $118.60. How many of each type were sold?

5. Write a system of equations for each of the following, and solve each of the systems.

i. A unique solution.

ii. An infinite number of solutions.

iii. No solution.

https://brainmass.com/math/linear-algebra/solving-systems-of-equations-29253

#### Solution Preview

1. Solve by substitution or elimination method:

3x - 2y = 8 (1)

-12x + 8y = 32 (2)

(1)*(-4): - 12x + 8y = -32 (3)

(3) + (2): 0 = 0

thus, (1) is equivalent to (2), there are infinite solutions.

2. Solve by substitution or elimination method:

7x - 5y = 14 (1)

-4x + y = 27 (2)

from (2): y = 4x+27 substitute into (1):

7x - 5(4x+27) = 14

7x-20x-135 = 14

-13x = 149

x = -149/13 = -11.46

then y = 4x+27= 4(-11.46)+27 = ...

#### Solution Summary

This shows how to solve systems of equations using substitution or elimination.

Graphing and linear equations

Please see attached for the complete details of the given problems:

WEEK HOMEWORK

Please add explanation and colored fonts on your answers

Page 483, #2

Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent.

Page 483, #6

Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent.

Page 483, #8

Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.

Page 483, #10

Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.

Page 483, #14

Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.

Page 484, #18

Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.

Page 484, #20

Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.

Page 484, #24

Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.

Page 485, #47

Perimeter of a rectangle. The length of a rectangular swimming pool is 15 feet longer than the width. If the perimeter is 82 feet, then what are the length and width?

Page 485, #48

Household income. Alkena and Hsu together earn $84, 326 per year. If Alkena earns $12,468 more per year than Hsu, then how much does each of them earn per year.

Individual Textbook Problems

Page 459, #20

Solve each system by graphing.

and

Page 461, #70

Solve each system by the substitution method.

and

Page 461, #92

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?

Page 471, #52

Solve each system by substitution or addition.

2y - x = 3

x = 3y - 5

Page 472, #72

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.

Discussion Questions Day 3

DQ1: True or False? Explain your answer. The equations y = 3x - 6 and y = 2x + 4 are independent.

DQ2: Which of the following equations is not equivalent to 2x - 3y = 6?

1) 3y - 2x = 6

2)

3)

4) 2(x - 5) = 3y - 4

DQ3: Which of the following equations is inconsistent with the equation 3x + 4y = 8?

1)

2) 6x + 8y = 16

3)

4) 3x - 4y = 8

- Discussion Questions Day 5

DQ1: True or False? Explain your answer. To solve the following system of equations by addition, we can multiply the first equation by 2 and the second by 3 and then add.

3x - y = 9

2x + y = 6

DQ2: True or False? Explain your answer. The solution set to the following system of equations is infinitely many solutions.

4x - 2y = 20

-2x + y = -10

DQ3: What is an inconsistent system? What happens if you attempt to solve such a system by graphing?

DQ4: When using the addition method, how can you tell if a system of linear equations has infinitely many solutions?

DQ5: When using the substitution method, how can you tell if a system of linear equations has no solution

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