# solutions for system of equations

Use the substitution method to find all solutions for the sytem of equations. Show work.

Question:

{2x +y = 7

{x + 2y = 2

Question:

{x^2 + y^2 = 25

{ y = 2x

Question:

{ x^2 + y = 9

{x - y + 3 = 0)

Question:

{ x^2 - y = 1

{2x^2 + 3y = 17

Use the elimination method to find all solutions of the system of equations. Show work.

Question:

{4x - 3y = 11

{8x + 4y = 12

Question:

{3x^2 + 4y=17

{2x^2 + 5y = 2

Question:

{2x^2 + 4y = 13

x^2 - y^2= 7/2

Question:

{x^2 - y^2 = 1

{2x^2-y^2 = x + 3

Find the determinant of the matrix, if it exists. Show any work.

Question:

[0 -1]

[2 0]

Question:

[-2 1]

[ 3 -2]

Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. Show work.

Question:

[0 -1 0]

[2 6 4]

[1 0 3]

Question:

[1 2 5]

[-2 -3 2]

[3 5 3]

Find the first four terms and the 100th term of the sequence. Show work.

Question:

an= 2n+3

Question:

an = n2 +1

Question:

an=1n^2

Question:

an = (-1)^n+1 n

------

n+1

Question:

an=3

Find the Sum (these have the symbols that look like a pointy E/properties of sums. Show work.

Question:

4

E (symbol) k2

k=1

Question:

100

E (symbol) (-1)^j

j=1

Question:

12

E (symbol) 10

i=4

Question:

3

E (symbol) i2^i

i=1.

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#### Solution Summary

The solution provides detailed explanation for many systems of equations.

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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