Expert: Richard J. Raridon - 2/7/2012

Question
Solving Systems 2
1.)Solve the system of equations: what is the y-value in the solution?
3x - 5y = -16 and 2x + 5y = 31
A. 5
B. 3
C. 2
D. 4

2.)Solve the system of equations.
5x - y = 3 and -10x + 2y = -6
A. (0, -3)
B. (-3, 0)
C. (3, 12)
D. no solution
E. infinitely many solutions

3.) Choose the correct first step(s) to solve the system using elimination.
4x + 7y = 6 and 6x + y = 2
A. 4x + 7y = 6 ? 4x + 7y = 6
(6x + y = 2)(-7)? -42x - 7y = -14
B. 4x + 7y = 6x + y
C. y = -6x + 2 ? 4x + 7(-6x + 2) = 6
D. (4x + 7y) + (6x + y) = 8
E. (4x + 7y) - (6x + y) = 4

4.) Solve the system of equations.
3x - 4y = -10 and 5x + 8y = -2
A. (1, 2)
B. (2, 1)
C. (1, -2)
D. (-2, 1)

5.) The sum of two numbers is 51. Their difference is 13. What is the smaller of the two numbers?
A. 18
B. 19
C. 20
D. 21

6.) Choose the correct first step(s) to solve the system using substitution.
y = 5x and 2x + 3y = 34
A. (- 5x + y = 0)(-3)? 15x - 3y = 0
2x + 3y = 34 ? 2x + 3y = 34
B. 2x + 3(5x) = 34
C. 5x = 2x + 3y
D. 5x + (2x + 3y) = 34
E. 5x - (2x - 3y) = -34

7.) Solve the system of equations.
6x + 2y = 10 and -6x - 2y = 12
A. (0, 5)
B. (-1, 8)
C. (2, -1)
D. no solution
E. infinitely many solutions

8.) Solve the system of equations.
4x + 7y = 6 and 6x + 5y = 20
A. (5, 2)
B. (-5, 2)
C. (5, -2)
D. no solution
E. infinitely many solutions

9.) Solve the system of equations: what is the x-value for the solution?
2x + 7y = 3 and x = 1 - 4y
A. -1
B. 5
C. 4
D. 3

10.) Charlotte has two job offers as a car sales person. The first job will pay her $600 a month plus 2% on the price of her car sales. The second job will pay $1000 a month plus 1% on the price of her sales. How much must she sell each month to make the same income from the two jobs?
A. $20,000
B. $30,000
C. $40,000
D. $50,000

Solving Systems 3
1.) Solve the system, using substitution. Write the solution as an ordered pair.
x = 2y - 2 and 3x - y = 14
A. (6, 4)
B. (4, 6)
C. (1, 0)
D. (0, 1)
E. no solution
2.) Solve the system, using substitution.
3a - b = 11 and 2a + 3b = 0
A. (3, 2)
B. (3, -2)
C. (-3, 2)
D. (-3, -2)
E. no solution
3.) Solve the system, using substitution. Write the solution as an ordered pair (m, n).
2m - 3n = 6 and m = 3 - 2n
A. (6, 2)
B. (3, 0)
C. (-3, -4)
D. (0, 2)
E. no solution
4.) Solve the system, using substitution.
4x + y = 4 and y = 4 - 4x
A. no solution
B. infinitely many solutions
5.) Solve the system, using substitution.
y = 1 - 5x and 5x + y = 8
A. no solution
B. infinitely many solutions
Solving Systems 4
1.) Solve the system by using elimination or elimination with multiplication.
2x + 3y = 12 and 3x + 2y = 13
A. (3, 2)
B. (-3, 2)
C. (-3, -2)
D. no solution
E. infinitely many solutions
2.) Solve the system by using elimination or elimination with multiplication. One point for the steps and one point for the correct solution.
3x + 4y = -2 and 2x - 3y = 10

3.) Solve the system by using elimination or elimination with multiplication. Write the solution as an ordered pair (a, b).
a - b = -5 and a + 2b = 1
A. (3, 2)
B. (3, -2)
C. (-3, -2)
D. (-3, 2)
E. no solution
4.) Solve the system by using elimination or elimination with multiplication.
x + y = 16 and x + y = -2
A. (8, 8)
B. (-2, 4)
C. (-1, -1)
D. no solution
E. infinitely many solutions
5.) Solve the system by using elimination or elimination with multiplication.
5x - 3y = 29 and x - 4y = 16
A. (4, 3)
B. (-4, 3)
C. (4, -3)
D. no solution
E. infinitely many solutions
6.) Solve the system by using elimination or elimination with multiplication. One point for the steps and one point for the correct solution
x - y = 3 and x + y = 7

7.) Solve the system by using elimination or elimination with multiplication.
3x - 2y = 9 and -3x + 2y = -9
A. (3, 0)
B. (5, 6)
C. (1, -3)
D. no solution
E. infinitely many solutions

Solving Systems 5
1.) Solve the following system using substitution or elimination: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Be sure to show all work.

2.) Write the solution to this problem as an ordered pair: To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all. How much is the membership fee and how much are the session?

3.) Solve the following problem using substitution or elimination: The sum of two numbers is 170 and their difference is 26. Be sure to show all work.

4.) Write a system of two equations with the variables m and f in each to represent the following problem: To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all.

5.) Write a system of two equations using x and y for the following problem: The sum of two numbers is 170 and their difference is 26. Find the two numbers.

6.) Solve the following problem using substitution or elimination: To skate at Roller Heaven, each person must pay a monthly membership fee (m) and a fee for each session (f). In January, Art attended 5 sessions and paid $25 in all. In July, he attended 10 sessions, and he paid $40 in all. How much is the membership fee and how much are the session? Be sure to show all work.

7.) Write the solution to the following problem as an ordered pair: The sum of two numbers is 170 and their difference is 26.

8.) Write two equations which represent the following two sentences: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x.

9.) Write the solution for the following problem as an ordered pair: The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Be sure to show all work.

10.) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?

Solving Systems 6
2.) Choose all correct answers. Which of the following are solutions of the system?
x < 3 and x + y < 5
A. (4, 2)
B. (2, 2)
C. (-1, 0)
D. (2, -1)
3.) Which of the following ordered pairs is included in the solution set of the system, y < 2 - 2x and y > 2x -3?
A. (0, 0)
B. (3, 4)
C. (4, 0)
D. No Solution
4.) Which ordered pair does not satisfy the system 2x + y > 0 and -2x - y > -8?
A. (3, -2)
B. (2, 3)
C. (-1, 4)
D. (-1, -1)
7.) Which one of the following is a solution of the system?
y <-1 and y > 8
A. (6, 9)
B. (-2, 4)
C. (0, 0)
D. No Solution

Solving Systems 7
1.) Mark and Nancy are making punch for a party and are using two types of juice: pineapple and papaya. The total number of quarts must be more than 9 but less than 15. They should use at least 4 quarts of each type. We want to find out how many quarts of each juice they should buy.
Pick one ordered pair solution for this problem and tell what each number represents.

2.) Mark and Nancy are making punch for a party and are using two types of juice: pineapple and papaya. The total number of quarts must be more than 9 but less than 15. They should use at least 4 quarts of each type. We want to find out how many quarts of each juice they should buy.
List any 3 ordered pair solutions for the system of equations which represent this problem.

3.) Mark and Nancy are making punch for a party and are using two types of juice: pineapple and papaya. The total number of quarts must be more than 9 but less than 15. They should use at least 4 quarts of each type. We want to find out how many quarts of each juice they should buy.
First graph the system below and describe the shape of the solution area.
X+Y>9
X+Y<15
X>4
Y>4

KNOWLEDGE CHECK
Solving Systems 3
1.) Which of the following ordered pairs is included in the solution set of the system?
y < 3/4 x + 3 and y > 3/4 x - 1
A. (0, 8)
B. (3, 4)
C. (9, 1)
D. No Solution

5.) Which ordered pair does not satisfy the system?
y <-2x + 9 and y > 3/4 x - 2
A. (3, -2)
B. (2, 3)
C. (-1, 4)
D. (-1, -1)

6.) (Choose all correct answers) Which of the following are solutions of the system?
y < 3 and x + y > 8
A. (9, 2)
B. (2, 2)
C. (10, 0)
D. (2, -1)

7.) Which one of the following is a solution of the system?
x + y < -3 and x + y > 8
A. (6, 9)
B. (-2, 4)
C. Infnitely Many Solutions
D. No solution

Solving Systems 8
1.) What are the dimensions of matrix A?
A= (First line)-2, 1, 0, 12,
(Right under it)3, 6, -9, 5
A. 2 X 2
B. 2 X 4
C. 4 X 4
D. 4 X 2

2.) Evaluate Q - P.
P= (First line) 8, -2
P=(right under) it 19, 6
P=(Right under second) 1, -13
Q=(First line) 6, 8
Q=(right under)0, 12
Q=(Right under second) 10, -4

3.) Evaluate C - D.
C=(First line)7, 11
C=(right under)-15, 3
D=(First line) 1, 0
D=(right under) 4, -11/2(Negative eleven over two)

Answer
Systems 2  1. A, 2. D, 3. A, 4. D, 5. B, 6. B, 7. D, 8. C, 9. B, 10. C
Systems 3  1. A, 2. B, 3. B, 4. B
Systems 4  1. A
2. 6x+4y=-4, 6x-9y=30, subtract to get 17y=-34 so y=-2, x=2,  3. D, 4. D
Systems 5 repeats
Systems 6  2. BCD, 3. (0,0), 4. D, 7. D
Systems 7  1. (5,5), 2. (5,5),(6,6),(7,7)
Knowledge Check 1. B, 5. A, 6. A&C, 7. D