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MAT 1033
PRACTICE TEST #2
NAME _______________________________
INSTRUCTOR M.BEYLIN
Determine whether the ordered pair is a solution of the system of linear equations.
1) (-6, -3);
x + y = -9
x - y = -3
1)
2) (-5, 2);
5x = -22 - y
x + 4y = 3
2)
Solve the system of equations by graphing.
x + 2y = 4
3)
3x - 2y = -12
3)
y
10
5
-10
-5
5
10
x
-5
-10
1
4)
x+y=5
x-y=3
4)
y
10
5
-10
-5
5
10
x
-5
-10
Without graphing, decide:
(a) Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point?
(b) How many solutions does the system have?
5) 3x - y = 8
5)
x + 4y = 20
6)
y - 3x = 5
6y = 18x + 30
6)
Solve the system of equations by the substitution method.
7) x + 5y = -21
-6x + 4y = -10
7)
8)
3x + y = 11
9x + 3y = 33
8)
9)
-5x - 15y = 9
5x + 15y = 0
9)
2
Solve the system of equations by the addition method.
10) x + 3y = 11
-6x + 2y = -6
11)
10)
2x - 3y = 2
3x - 5y = 2
11)
x
y
+
=1
5 15
12)
13)
12)
x
y
=0
4 12
5x -
3
y = -26
4
3x +
2
44
y=5
5
13)
3
Write a system of equations in x and y describing the situation. Do not solve the system.
14) One number is 5 more than another number. If you add 8 to 2 times the first number, the
result is 3 times the second number.
14)
15) The sum of two numbers is -5. Three times the first number equals 4 times the second
number. Find the two numbers.
15)
16) The three angles in a triangle always add up to 180°. If one angle in a triangle is 110° and
the second is 4 times the third, what are the three angles?
16)
17) A chemist needs 70 milliliters of a 55% solution but has only 40% and 61% solutions
available. Find how many milliliters of each that should be mixed to get the desired
solution.
17)
18) Jimmy is a partner in an Internet-based coffee supplier. The company offers gourmet
coffee beans for $12 per pound and regular coffee beans for $6 per pound. Jimmy is
creating a medium-price product that will sell for $8 per pound. The first thing to go into
the mixing bin was 10 pounds of the gourmet beans. How many pounds of the less
expensive regular beans should be added?
18)
Solve.
4
19) Dmitri needs 7 liters of a 36% solution of sulfuric acid for a research project in molecular
biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the
56% solution and the other an unlimited supply of the 21% solution. How many liters of
each solution should Dmitri use?
19)
20) Natasha rides her bike (at a constant speed) for 4 hours, helped by a wind of 3 miles per
hour. Pedaling at the same rate, the trip back against the wind takes 10 hours. Find find the
total round trip distance she traveled.
20)
Determine whether the ordered pair given is a solution of the linear inequality in two variables.
21) x + 2y > -10; (3, -6)
21)
22) x ≤ y - 3; (-2, -1)
22)
5
Graph the solution of the system of linear inequalities.
x ≥ 2y
23)
x + 2y ≤ 6
23)
y
10
5
-10
-5
5
10
x
-5
-10
24)
y<
1
x+8
2
y>
1
x+1
2
24)
y
10
5
-10
-5
5
10
x
-5
-10
6
25)
x≥-1
5x + 4y ≤ -3
25)
y
10
5
-10
-5
5
10
x
-5
-10
Solve the problem.
26) Bruce is a retired carpenter who builds patio chairs and dog houses, which he sells at his
local flea market. It takes him 3 hours to build a dog house and 4 hours to build a patio
chair. Bruce can work no more than 25 hours per week, and he must produce more chairs
than dog houses. Write a system of inequalities to describe this situation. Use D for the
number of dog houses and P for the number of patio chairs produced in a week.
7
26)
Answer Key
Testname: 1033 EXAM2 REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
Yes
No
(-2, 3)
(4, 1)
lines intersecting at a single point; one solution
identical lines; infinite number of solutions
(-1, -4)
infinite number of solutions
no solution
(2, 3)
(4, 2)
5 15
12)
,
2 2
13) (-4, 8)
14) x - y = 5
2x - 3y = -8
20
15
15) and 7
7
16)
17)
18)
19)
20)
21)
22)
23)
110°, 56°, 14°
20 ml of 40%; 50 ml of 61%
20 lb
56% solution: 3 L; 21% solution: 4 L
80 mi
Yes
No
y
10
5
-10
-5
5
10
x
-5
-10
8
Answer Key
Testname: 1033 EXAM2 REVIEW
24)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
25)
y
10
5
-10
-5
-5
-10
26)
P>D
4P + 3D ≤ 25
9