o 28.
b + 2a = 2,
a = −3 − b
o 16.
5x+6y=14
-3y+x=7
o 26. Ink remover. Etch Clean Graphics uses one cleanser that is 25% acid and a second that is 50%
acid. How many liters of each should be mixed to get 30 L of a solution that is 40% acid?
2. Determine whether the point (0, 8) is a solution of the system
-3x + 9y = 72
9x + 3y = 24
by substituting the point into each equation.
0 1357669423 Essay 1
3. The point (22, 0) lies on the line -x – 8y = -22. Determine if this point is a solution of the
system
-x – 8y = -22
-7x + 3y = -36
(
0 1357669424 Essay 16
4. Solve using the elimination method. Show your work. If the system has no solution or an
infinite number of solutions, state this.
-3x – 8y = -88
-3x – 2y = -40
0 1357669426 Essay 22
5. Solve using the elimination method. Show your work. If the system has no solution or an
infinite number of solutions, state this.
-5x + 4y = -16
-15x + 2y = -58
0 1357669427 Essay 40
6. Select the set of equations that represents the following situation: The sum of two numbers is 61, and
their difference is sixteen more than the smaller number. What are the two numbers?
(Points : 3)
2x = 61; 61 = x + 16
2y = 61; 61 = x – 16
x + y = 61; y – x = x + 16
x + y = 61; x – y = 16 – x
0 1357669428 MultipleChoice 14
7. Select the set of equations that represents the following situation: Mike invested $604 for one year. He
invested part of it at 6% and the rest at 3%. At the end of the year he earned $29.91 in interest. How much
did Mike invest at each rate of interest?
(Points : 3)
0.06x + 0.03y = 604; x + y = 29.91
x + y = 604; 6x + 3y = 29.91
x + y = 604; 0.06x + 0.03y = 29.91
0.06 · 604 + 0.03 · 604 = 29.91
0 1357669429 MultipleChoice 25
8. A university bookstore recently sold a wirebound graph-paper notebook for $2.55, and a college-ruled
notebook for $3.22. At the start of spring semester, a combination of 50 of these notebooks were sold for a
total of $157.65. How many of each type were sold?
2. Solve using the substitution method. Show your work. If the system has no solution or
an infinite number of solutions, state this.
-8x – 4y = -68
x + 3y = 16
0 1357678368 Essay 8
3. Solve using the elimination method. Show your work. If the system has no solution or an
infinite number of solutions, state this.
-3x + 4y = 1
-6x + 6y = -3
0 1357678370 Essay 11
4. Solve using the elimination method. Show your work. If the system has no solution or an
infinite number of solutions, state this.
-8x – 2y = -28
-3x + 5y = 47
0 1357678371 Essay 29
5. Solve using the elimination method. Show your work. If the system has no solution or an
infinite number of solutions, state this.
5x – 4y = 10.5
20x – 16y = 42
0 1357678374 Essay 34
6. Select the set of equations that represents the following situation: The cost of eleven CDs and seven
DVDs is $172.75; and the cost of ten DVDs and seven CDs is $162.69. How much do a CD and a DVD cost?
(Points : 3)
11x · 7y = 172.75; 13x · 7y = 162.69
11x + 7y = 172.75; 7x + 10y = 162.69
11x + 7y = 172.75; 10x + 7y = 162.69
11x · 7y = 172.75; 10x · 7y = 162.69
0 1357678376 MultipleChoice 3
7. Select the set of equations that represents the following situation: Mary invested one amount at 7%
simple interest, and a second amount at 10% interest, earning $58.00 in one year. If she had switched the
amounts, she would have earned $56.92. What were the two amounts?
(Points : 3)
0.07x + 0.10y = 56.92; 0.07x + 0.10y = 58.00
0.07x + 0.10y = 58.00; 0.07y + 0.10x = 56.92
7x + 10y = 58.00; 7y + 10x = 56.92
7x + 10y = 56.92; 7x + 10y = 58.00
0 1357678380 MultipleChoice 15
8. To buy both a new car and a new house, Tina sought two loans totalling $44,980. The simple interest
rate on the first loan was 1.8%, while the simple interest rate on the second loan was 1.2%. At the end of
the first year, Tina paid a combined interest payment of $679.64. What were the amounts of the two
loans?
0 1357678381 Essay 46
9. A dehydrated patient needs a 3.24% saline IV. Unfortunately, the hospital only has bags of 1% and 9%
saline solutions. How many liters of each of these solutions should be mixed together to yield 5 liters of the
desired concentration?
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