Exam 2 Review Math1324 Solve the system of two equations in two variables. 1) 8x + 7y = 36 3x - 4y = -13 A) (1, 5) B) (0, 5) C) No solution D) (1, 4) 2) 3x + 5y = 4 18x + 30y = 24 A) - 1 3 , 1 B) No solution C) - 5 3 y + 4 3 , y for any real number y D) 4 3 , 0 Solve the problem by writing and solving a suitable system of equations. 3) If 20 pounds of tomatoes and 10 pounds of bananas cost $17 and 40 pounds of tomatoes and 30 pounds of bananas cost $39, what is the price per pound of tomatoes and bananas? A) tomatoes: $0.70 per pound; bananas: $0.30 per pound B) tomatoes: $0.60 per pound; bananas: $0.50 per pound C) tomatoes: $0.70 per pound; bananas: $0.50 per pound D) tomatoes: $0.50 per pound; bananas: $0.70 per pound Solve the system by back substitution. 4) x + 4y+ 4z = -11 2y + 5z = -21 2z = - 10 A) (1, -5, 2) B) (1, 2, -5) C) (-6, 2, -5) D) No solution Obtain an equivalent system by performing the stated elementary operation on the system. 5) Replace the fourth equation by the sum of itself and 3 times the second equation x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 5y - 5z - 2w= 8 A) x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 12y + 3z - 14w= -7 B) x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 17y - 8z - 14w= -7 C) x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 -7y + 8z + 10w = 23 D) x - 2y + 5z - 6w = 4 12y - 3z - 12w= -15 3y - 4z + 2w = -3 5y - 5z - 2w= 8 1
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Exam 2 Review Math1324
Solve the system of two equations in two variables.
1) 8x + 7y = 36
3x - 4y = -13
A) (1, 5) B) (0, 5) C) No solution D) (1, 4)
2) 3x + 5y = 4
18x + 30y = 24
A) - 1
3, 1 B) No solution
C) - 5
3y +
4
3, y for any real number y D)
4
3, 0
Solve the problem by writing and solving a suitable system of equations.
3) If 20 pounds of tomatoes and 10 pounds of bananas cost $17 and 40 pounds of tomatoes and 30 pounds of
bananas cost $39, what is the price per pound of tomatoes and bananas?
A) tomatoes: $0.70 per pound; bananas: $0.30 per pound
B) tomatoes: $0.60 per pound; bananas: $0.50 per pound
C) tomatoes: $0.70 per pound; bananas: $0.50 per pound
D) tomatoes: $0.50 per pound; bananas: $0.70 per pound
Solve the system by back substitution.
4) x + 4y+ 4z = -11
2y + 5z = -21
2z = - 10
A) (1, -5, 2) B) (1, 2, -5) C) (-6, 2, -5) D) No solution
Obtain an equivalent system by performing the stated elementary operation on the system.
5) Replace the fourth equation by the sum of itself and 3 times the second equation
x - 2y + 5z - 6w = 4
4y - z - 4w = -5
3y - 4z + 2w = -3
5y - 5z - 2w = 8
A)
x - 2y + 5z - 6w = 4
4y - z - 4w = -5
3y - 4z + 2w = -3
12y + 3z - 14w = -7
B)
x - 2y + 5z - 6w = 4
4y - z - 4w = -5
3y - 4z + 2w = -3
17y - 8z - 14w = -7
C)
x - 2y + 5z - 6w = 4
4y - z - 4w = -5
3y - 4z + 2w = -3
-7y + 8z + 10w = 23
D)
x - 2y + 5z - 6w = 4
12y - 3z - 12w = -15
3y - 4z + 2w = -3
5y - 5z - 2w = 8
1
Write the system of equations associated with the augmented matrix. Do not solve.
6)1 0 0 -8
0 1 0 3
0 0 1 -3
A) x = 0
y = -5
z =-11
B) x = -5
y = 6
z = 0
C) x = 8
y = -3
z = 3
D) x = -8
y = 3
z = -3
The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the
system.
7)
1 0 0 0 0 3
0 1 0 0 0 8
0 0 1 0 0 6
0 0 0 1 0 -6
0 0 0 0 0 1
A) (3, 8, 6, -6, w) for any real number w B) (3, 8, 6, -6)
C) (3, 8, 6, -6, 1) D) No solution
8)
1 0 0 0 13
0 1 0 0 0
0 0 1 0 -8
0 0 0 1 11/2
A) 13, -8, 11
2, 0 B) No solution
C) 13, 0, -8, 11
2D) 13, w, -8,
11
2 for any real number w
Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent,
dependent, or inconsistent.
9) x + y - 2z = 8
3x + z = - 6
2x - y + 3z = -14
A) Independent B) Dependent C) Inconsistent
Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.
10) 2x + y - z = 2
x - 3y + 2z = 1
7x - 7y + 4z = 7
A)7 + z
7,
5
7z, z for any real number z B) (1, 0, 0)
C) (2, 5, 7) D) No solution
2
Solve the problem by writing and solving a suitable system of equations.
11) Alan invests a total of $20,500 in three different ways. He invests one part in a mutual fund which in the first
year has a return of 11%. He invests the second part in a government bond at 7% per year. The third part he
puts in the bank at 5% per year. He invests twice as much in the mutual fund as in the bank. The first year
Alan's investments bring a total return of $1645. How much did he invest in each way?
A) mutual fund: $7000; bond: $11,000: bank: $3500 B) mutual fund: $7000; bond: $10,000: bank: $3500