Download Unit 2 Review File

Name Class Date Practice
Form K
Solving Equations
Solve each equation.
1. 5x + 4 = 2x + 10
To start, subtract 2x from each side.
2. 10w - 3 = 8w + 5
To start, subtract 8w from each side.
4. s + 2 - 3s - 16 = 0
3. 4(d - 3) = 2d
Solve each equation. Check your answer.
5. 9(z - 3) = 12z
6. 7y + 5 = 6y + 11
7. 5w + 8 - 12w = 16 - 15w
8. 3(x + 1) = 2(x + 11)
Write an equation to solve each problem.
9. Lisa and Beth have babysitting jobs. Lisa earns $30 per week and Beth earns
$25 per week. How many weeks will it take for them to earn a total of $275?
To start, record what you know.
Describe what you need to find.
Lisa earns $30 per week.
Beth earns $25 per week.
Total earned: $275
an equation to find the number of
weeks it takes to earn $275 together
10. The angles of a triangle are in the ratio 2 : 12 : 16. The sum of all the angles in a
triangle must equal 180 degrees. What is the degree measure of each angle of
the triangle? Let x = the common factor.
11. What two consecutive numbers have a sum of 53?
Determine whether the equation is always, sometimes, or never true.
12. 3(2x - 4) = 6(x - 2)
13. 4(x + 3) = 2(2x + 1)
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Name Class Date Practice (continued)
Form K
Solving Equations
Solve each formula for the indicated variable.
14. A = 1
2bh, for b
15. P = 2w + 2l, for w
16. A = 1
2h(b1 + b2), for h
17. S = 2prh + 2pr 2 , for h
Solve each equation for y.
18. ry - sy = t
3
19. 7(y + 2) = g
y
20. m + 3 = n
21.
3y - 1
2 =z
Solve each equation.
22. (x - 3) - 2 = 6 - 2(x + 1)
23. 4(a + 2) - 2a = 10 + 3(a - 3)
24. 2(2c + 1) - c = -13
25. 8u + 2(u - 10) = 0
26. The first half of a play is 35 minutes longer than the second half of the play. If
the entire play is 155 minutes long, how long is the first half of the play? Write
an equation to solve the problem.
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Name Class Date Practice
Form K
Solving Inequalities
Write the inequality that represents the sentence.
1. Five less than a number is at least -28.
2. The product of a number and four is at most -10.
3. Six more than a quotient of a number and three is greater than 14.
Solve each inequality. Graph the solution.
4. 5a - 10 7 5
5. 25 - 2y Ú 33
To start, add 10 to each side.
6. -2(n + 2) + 6 … 16
7. 2(7a + 1) 7 2a - 10
Solve the following problem by writing an inequality.
8. The width of a rectangle is 4 cm less than the length. The perimeter is
at most 48 cm. What are the restrictions on the dimensions of the rectangle?
To start, record what you know.
width: length - 4
perimeter: at most 48 cm
Describe what you need to find.
restrictions on the width and
length of the rectangle
Is the inequality always, sometimes, or never true?
9. 5(x - 2) Ú 2x + 1
11. 6x + 1 6 3(2x - 4)
10. 2x + 8 … 2(x + 1)
12. 2(3x + 3) 7 2(3x + 1)
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Name Class Date Practice (continued)
Form K
Solving Inequalities
Solve each compound inequality. Graph the solution.
13. 2x 7 -4 and 4x 6 12
To start, simplify each inequality.
x 7 -2 and x 6 3
Remember, “and” means that a solution makes BOTH inequalities true.
14. 3x Ú -12 and 5x … 5
15. 6x 7 6 and 9x … 45
Solve each compound inequality. Graph the solution.
16. 3x 6 -9 or 8x 7 -8
To start, simplify each inequality.
x 6 -3 or x 7 -1
Remember, “or” means that a solution makes EITHER inequality true.
17. 7x … -28 or 2x 7 -2
18. 3x 7 3
or
5x 6 2x - 3
Write an inequality to represent each sentence.
19. The average of Shondra’s test scores in Physics is between 88 and 93.
20. The Morgans are buying a new house. They want to buy either a house more
the 75 years old or a house less than 10 years old.
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Name Class Date Practice
Form G
Linear Functions and Slope-Intercept Form
Find the slope of the line through each pair of points.
( )
(
)
1. (0, 1) and (3, 0)
3 5
2
2. 1
2, 3 and - 2 , 3
3. (-3, -2) and (1, 6)
4. (4, -1) and (-2, -3)
5. (3, -5) and (1, 2)
6. (8, 9) and (8, 3)
7. (-3, -3) and (-1, -3)
1
8. 1
2, 2 and (-2, -4)
( )
Write an equation for each line.
9. m = -4 and the y-intercept is 3.
11. m = 0 and the y-intercept is -4.
17
10. m = 2
5 and the y-intercept is 5 .
12. m = -1 and the y-intercept is 2.
Find the slope and y-intercept of each line.
13.
14.
y
4
y
2
2
x
!4
!2
O
2
4
!4
!2
O
2
4x
!2
!4
!4
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Name Class Date Practice (continued)
Form G
Linear Functions and Slope-Intercept Form
Find the slope and y-intercept of each line.
15. 3x - 4y = 12
16. y = -2
5
17. f (x) = 4 x + 7
18. x = 5
19. 4x - 3y = -6
20. g(x) = -3x - 17.5
Graph each equation.
x y
22. 3 - 6 = 1
21. 4x + 3y = 12
3
23. y = - 2 x + 1
2
Find the slope and y-intercept of each line.
24.
25.
y
26.
y
2
2
2
2
x
x
x
!2
y
!2
O
2
!2
!2
!2
O
!2
27. The equation e = 1200 + 11t represents your elevation e in feet for each
minute t you hike from a trailhead.
a. If you graphed this equation, what would the slope represent? Explain.
b. Are you hiking uphill or downhill? Explain.
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2
Kuta Software - Infinite Algebra 2
Name___________________________________
Systems of Two Equations
Date________________ Period____
Solve each system by graphing.
1) y = −3 x + 4
y = 3x − 2
−5
−4
−3
−2
2) y = x + 2
x = −3
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
3) x − y = 3
7 x − y = −3
−5
−5
1
2
3
4
5
1
2
3
4
5
4) 4 x + y = 2
x− y=3
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
Solve each system by substitution.
5) y = 4 x − 9
y=x−3
6) 4 x + 2 y = 10
x − y = 13
7) y = −5
5 x + 4 y = −20
8) x + 7 y = 0
2 x − 8 y = 22
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-1-
Worksheet by Kuta Software LLC
Name Class Date Practice
Form G
Solving Systems Algebraically
Solve each system by substitution. Check your answers.
1. e
4. e
7. e
y=x+1
2x + y = 7
6x - 3y = -33
2x + 3y = -1
x + 3y = -4
y + 3x = 0
2. e
5. e
8. e
x=y-2
3x - y = 6
2x - 2y = 7
3x - 2y = 10
3x + 2y = 9
3x + 2y = 3
3. e
6. e
9. e
y = 2x + 3
5x - y = -3
4x = 8y
2x + 5y = 27
2y - 3x = 4
x = -4
10. Suppose you bought eight oranges and one grapefruit for a total of $4.60. Later
that day, you bought six oranges and three grapefruits for a total of $4.80.
What is the price of each type of fruit?
Solve each system by elimination.
11. e
14. e
17. e
x + y = 10
x - y = 12
12. e
4x - 3y = -2
4x + 5y = 14
15. e
x-y=0
x+y=2
18. e
-x + 3y = -1
-x - 2y = -2
3x + 2y = 10
3x - 2y = 19
x + 3y = - 4
x+ y= 0
13. e
16. e
19. e
x + 3y = 17
x + 3y = 11
2x - 15y = 11
4x + 10y = 18
3x - y = 17
2x + y = 18
20. There are a total of 15 apartments in two buildings. The difference of two times the
number of apartments in the first building and three times the number of apartments in
the second building is 5.
a. Write a system of equations to model the relationship between the number
of apartments in the first building f and the number of apartments in the second
building s.
b. How many apartments are in each building?
Solve each system by elimination.
21. e
24. e
27. e
-x + y = 3
5x + y = 9
22. e
14x + 2y = 10
14x - 5y = 11
4x + 3y = -6
5x - 6y = -27
25. e
28. e
-5x + 4y = 2
-5x - 2y = 4
2x + 15y = 1
2x + 10y = 2
2x + 2y = -10
4x + 2y = -11
23. e
26. e
29. e
-2x + y = -3
-5x - y = -3
0.3x + 0.4y = -0.8
0.7x - 0.8y = -6.8
1.2x + 1.4y = 2.7
0.4x - 0.3y = 0.9
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Name Practice
Class Date Form G
(continued)
Solving Systems Algebraically
30. Writing Explain what it means when elimination results in an equation that is
always true.
For each system, choose the solution method that seems easier to use. Explain
why you made each choice. Solve each system.
31. e
33. e
b = 2a - 5
b=3+a
32. e
5p + 2q = 10
4p + 2q = 4
34. e
4x - 2y = 11
4x + 3y = 6
j - 3k = 3
j = -k + 15
35. Error Analysis You and your friend are solving the system 4x - y = 5 and
4x + y = 3. Your friend says there is no solution, and you say the solution is
(1, -1). Who is correct? Explain.
36. You can buy DVDs at a local store for $15.49 each. You can buy them at an
online store for $13.99 each plus $6 for shipping. How many DVDs can you
buy for the same amount at the two stores?
37. Last year, a baseball team paid $20 per bat and $12 per glove, spending a total
of $1040. This year, the prices went up to $25 per bat and $16 per glove. The
team spent $1350 to purchase the same amount of equipment as last year.
How many bats and gloves did the team purchase each year?
38. If the perimeter of the square at the right is 72 units, what are
3y
the values of x and y?
2x
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Name Class Date Practice
Form G
Systems With Three Variables
Solve each system by elimination. Check your answers.
x + y + z = -1
1. W 2x - y + 2z = -5
-x + 2y - z = 4
x - y + 2z = 10
2x + 2y + 2z = 3
2. W 2x - 2y + 2z = 6
3x + 2y - 2z = 13
2x - y + z = -4
2x + y = 9
3. W x - 2z = -3
2y + 3z = 15
2x - y - z = 4
4. W -x + y - 2z = 5
5. W 3x + y - 2z = 0
6. W -x + 2y + z = 1
x + 5y + 5z = -10
7. W x + 5y + 5z = 2
x + 2y + 3z = -3
x-y-z=0
8. W x - 2y - 2z = 3
-2x + 2y - z = 3
3x + 2y + 2z = 6
9. W 3x - 2y + 2z = 14
3x + 3y - 3z = -6
2x + 2y + 3z = -2
10. W 2x + 2y - 3z = 11
3x - 2y + 3z = 4
2x - 5y + z = 3
11. W 2x + 2y - 2z = -12
2x + 2z = 6
3x - 3y + 6z = -2
3x - y = -4
3x + y + z = 16
2x + 3z = 2
12. W 3x + 6y = 6
3x - 2z = 8
Solve each system by substitution. Check your answers.
3x + y - z = 0
13. W 3x - y + z = 4
5x + z = 7
2x - 2y = 1
14. W 2x + 3y + z = 0
2x - 2z = 18
x + y + 4z = 5
15. W -2x + 2z = 3
3x + y - 2z = 0
-3x + 2y + 2z = 4
16. W -6x + 4y - 2z = -9
-9x - 2y + 2z = 10
2x - 3y + z = -3
17. W x - 5y + 7z = -11
-10x + 4y - 6z = 28
2x + 3y + 2z = -8
18. W 2x - 3y - 2z = 6
2x - 3y + 2z = -1
14x - 3y + 5z = -15
19. W 13x + 2y - 6z = 10
17x - 2y + 4z = -5
5x - 3y + 2z = 39
20. W 4x + 4y - 3z = 34
3x - 2y + 6z = 14
x+y+z=6
21. W 2x - y + 2z = 6
-x + y + 3z = 10
2x + y - z = 3
22. W 3x - y + 3z = 3
-x - 3y + 2z = 3
-2x - 3y + 3z = 4
23. W -2x + 3y - 3z = -4
-6x - 9y + 3z = 12
2x + y - z = 1
24. W 2x + 2z = 3
2x + 2y = 4
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