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Algebra I – Chapter 5 Test Review
Standards/Goals:
 A.CED.3: I can interpret the solutions of equations and inequalities.
 A.REI.11: I can represent the solutions of a system graphically, and use technology to graph the
system.
 A.REI.6: I can solve a system of linear equations by graphing.
 D.1.g: I can solve systems of equations in a variety of methods, including: graphing,
substitution and elimination.
True/False. Explain false.
Refer to the figure below to answer the following equations:
#1. The system of equations shown below would have one solution and it would be (-2, 0)
3x – 3y = −6
{
y = −x – 2
#2. The system of equations shown below would have one solution and it would be (0, 2)
3x – y = 2
{
y = −x– 2
#3. The system of equations shown below would have infinitely many solutions.
y = −x– 2
{
x + y = 0
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Solving Systems
#1.
Use substitution to solve the system:
x = 2y + 3
{
4x – 5y = 9
#2.
Use elimination to solve the system:
x + 7y = 16
{
3x – 7y = 4
#3.
Use elimination to solve the system:
x – 5y = 20
{
x + 3y = −4
#4.
Use elimination to solve the system:
8x – 7y = 5
{
3x – 5y = 9
#5.
Use any method to solve the following system:
3
{
#6.
y = 3x + 3
y = −1/2 x + −1/2
Use any method to solve the following system:
4x + 6y = 10
{
2x + 5y = 1
Graphing Systems
On the graphs provided, graph each of the following system of equations. Then determine
whether the system has no solution, one solution, or infinitely many solutions. If the system
has one solution, name it.
y = −x + 2
#1.
{
3x + 3y = −3
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#2.
{
x + 2y = 3
3x – y = −5
#3. This is the graph of ⃡𝑃𝑄 ?
What is the point of intersection of line PQ and the line whose equation is y = -x – 7?
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Solve each equation
#1. 4n – 2n = 4
#2. -12 = 2 + 5v + 2v
#3. 3 = x + 3 – 5x
#4. x + 3 – 3 = -6
#5. -12 = 3 – 2k – 3k
#6. -1 = -3r + 2r
#7. 6 = -3(x + 2)
#8. -3(4r – 8) = -36
#9. 24 = 6(-x – 3)
#10. 75 = 3(-6n – 5)
#11. 10p + 9 – 11 – p = -2(2p + 4) – 3(2p – 2)
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#12. -10n + 3(8 + 8n) = -6(n – 4)
#13. 10(x + 3) – (-9x – 4) = x – 5 + 3
#14. 12(2k + 11) = 12(2k + 12)
#15. 2x + 4  3x = 5  x
Solve each formula for the indicated variable.
#1. 3m – n = 2m + n, for m
#3. F 
G  m1  m2
, for G
d2
1
3
2
#2. V   r h, for h
#4.
1
r + 3s = 1, for r
2
7
#5.
2
5
f  g  1  fg , for f
3
12
#6.
xk 3
 , for x
j
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FLASHBACK SECTION:
Solve each inequality, graph the solution and write an interval for its solution.
#1. -5x > 70
#2. -8 < 2x – 6 ≤ 18
#3. -2|𝑥 + 5| + 10 > −22
#4. 10 + |𝑥 + 9| < 8
#5. −4|8𝑥 − 9| > 20
#6. |𝑥 + 7| + 18 = 17
#7. 10 + |𝑥 − 40| = 7
#8. −2|𝑥| ≥ 8
#9. 9|𝑥| ≥ 18
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#10. Evaluate each expression for the given values of the variables.
a. 6c + 5d  4c  3d + 3c  6d; c = 4 and d = 2
b. 10a + 3b  5a + 4b + 1a + 5b; a = 3 and b = 5
c.
3m + 9n + 6m  7n  4m + 2n; m = 6 and n = 4
#11. What are domain for the relation: 𝑦 =
𝑥+8
?
𝑥−8
#12. Evaluate f(g(x)) when x = 6.
f(x) = 2x – 4
y – 8 = ¾ (x + 6)
g(x) =
𝒙
𝟑𝒙 − 𝟒
#13. Consider :
Write the equation in slope intercept and in standard form. What would the slope be of a line both
parallel and perpendicular to the line modeled by that equation?
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#14. Determine the domain and range of the following graphs. Additionally, determine if the relation
is a function or not.
#15. Which 2 quadrants in the Cartesian coordinate plane contain the line whose equation is: y + 8 = 0?
#16. Which 2 quadrants in the Cartesian coordinate plane contain the line whose equation is: y – 9 = 0?
#17. Which 2 quadrants in the Cartesian coordinate plane contain the line whose equation is: x – 4 = 0?
#18. Which 2 quadrants in the Cartesian coordinate plane contain the line whose equation is: x + 2 = 0?
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#19. Write an equation that would be in standard form and would be parallel to each of the following
equations:
5x + 7y = 1
-5x + 3y = 12
-6x + 7y = 13
-4x + 28y = 20
#20. What is the equation, in standard form, of the line that passes through (10, -6) and has a
slope of ½?
#21. What is the equation, in standard form, of the line that passes through (10, -6) and has a
slope of 2/3?
#22. Write some examples of equations that have positive, negative, zero and NO slope: