Questions:
Explanation and colored fonts on your answers
1. Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent.
y = 3x -4
y = -2x +1
2. Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent.
3x -y = 4
3x -y = 0
3. Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.
x-y =3
3x-2y = 3
4. Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.
3y + x+5
3x-9y = -10
5. Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent.
x = 1/8y-1
y = 1/4x+39
6. Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.
-3x+y = 3
2x_3y =5
7. Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.
x+3(y-1) = 11
2(x-y)+8y=28
8. Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent.
1/3x - 1/6 y = 1/3
1/6x + 1/4 y = 0
9. 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?
10. 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
11. Solve each system by graphing.
y = -2/3x
and
2x+3y = 5
12. Solve each system by the substitution method.
x + 3y = 2
and
-x + y = 1
13. 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?
14. Solve each system by substitution or addition.
2y - x = 3
x = 3y - 5
15. 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 Question
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) y = 2/3x - 2
3) x = 3/2y+3
4) 2(x - 5) = 3y - 4
DQ3: Which of the following equations is inconsistent with the equation 3x + 4y = 8?
1) y = 3/4x + 2
2) 6x + 8y = 16
3) y = -3/4x + 8
4) 3x - 4y = 8
DQ4: 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
DQ5: 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
DQ6: What is an inconsistent system? What happens if you attempt to solve such a system by graphing?
DQ7: When using the addition method, how can you tell if a system of linear equations has infinitely many solutions?
DQ8: When using the substitution method, how can you tell if a system of linear equations has no solution