Algebra I Part 2
Unit 1 Study Guide – Systems of Equations and Inequalities
p1
Fill in the blanks:
1.
2.
3.
4.
5.
6.
7.
8.
“greater than” symbol _____
“greater than or equal to” symbol _____
“less than” symbol _____
“less than or equal to” symbol _____
A system with infinitely many solutions means that the lines ______________
A system with no solution means that the lines ______________
A system with one solution means that the lines ______________
______________ divide the coordinate plane into two half planes
Determine if system of equations is consistent or inconsistent and independent or
dependent.
y
9.
y = -4x – 1
10.
3x – 4y = 8

3
x 1
4
3x – 4y = 8
y



x











11.
y = -2x + 3
12.
y = -4x – 1
3x – 4y = 8
3
y  x 2
4


Solve each system using graphing. You must graph both lines on the grid provided.
13.
y = 4x
SOLUTION: _________
y = – x + 10
10
14.
x + 4y = 8
1
y   x5
4
SOLUTION: _________
y
10
8
8
6
6
4
4
2
y
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8
10
Algebra I Part 2
Unit 1 Study Guide – Systems of Equations and Inequalities
15.
p2
Solve the system of inequalities by graphing the solution set. Use the coordinate plane provided.
y<x+1
y > 2x
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
16.
Is (4, 7) a solution to the following system of
equations?
3x + y = 11
y=x+3
18.
Bill’s Discount Cinema sold adult tickets for $5.60 each and children’s tickets for $4.50 each. A total of 25
tickets were sold for a total collected amount of $114.80. Write the system of equations that could be
used to find the number of each type of ticket (adult & children’s) sold.
19.
Is the point (0, -3) in the solution region for
the system of inequalities shown below?
x – 2y  6
3x – 2y > 6
17.
20.
Is (1, -5) the solution to the following system
of equations?
y = -3x – 2
6x + 2y = -4
Is the point (1, 2) in the solution region for
the system of inequalities shown below?
y < ½x + 2
2
y<- x–1
3
Algebra I Part 2
Unit 1 Study Guide – Systems of Equations and Inequalities
21.
Solve the following systems of equations using
substitution:
2x + y = 4
y=x+1
23.
22.
Solve the following system of equations using
substituation:
Solution: _____________
x – 2y = -7
2x + 3y = 21
Solve the following system of equations using
elimination:
3x – 4y = 10
5x + 4y = 6
p3
Solution: _____________
24.
Solution: _____________
Solve the following system of equations using
elimination:
5x – 3y = 1
x + 2y = 8
Solution: _____________
25. A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 4 bags of potato chips for
$17.25. Another customer buys 2 hot dogs and 2 bags of potato chips for $7.50. Find the cost of each item.
Set up a system of equations, then solve by elimination.
$_____ for each hot dog and $_____ for each bag of chips
26. Discuss how you decide when you should solve a system of equations by the graphing method, the substitution
method, and by the elimination method. Make sure you discuss all three methods.
Algebra I Part 2
Unit 1 Study Guide – Systems of Equations and Inequalities
Answer Key:
1. >
2. ≥
3. <
4. ≤
5. are the same lines
6. are parallel
7. intersect
8. boundary lines
9. consistent and independent
10. inconsistent
11. consistent and independent
12. consistent and dependent
13. (2, 8) – see graph to the right
14. No Solution (lines are parallel) – see graph to the right
15.
10
p4
13.
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
2
4
6
8
10
-2
-4
-6
-8
-10
14.
10
y
8
y
6
4
8
2
6
x
-10
4
-8
-6
-4
-2
-2
-4
2
-6
x
-10
-8
-6
-4
-2
2
-2
4
6
8
10
-8
-10
-4
-6
-8
Shaded Region
(below the dashed and above the solid boundary)
-10
16. no
17. yes
18.
a + c = 25
5.60a + 4.50c = 114.80
19. no
20. no
21. (1, 2)
22. (3, 5)
23. (2, -1)
24. (2, 3)
25.
5h + 4c = 17.25
2h + 2c = 7.50
Hot dog = $2.25
Chips = $1.50
26.
(Answers may very. Some examples follow.)
If in slope-intercept form, graphing
If one equation has only one variable or is already solved for a variable, substitution
If in standard form, elimination