Download Algebra Chapter 7 - Rochester Community Schools

Algebra Chapter 7 – Review
Show ALL your work!
Name _________________________________
Hour ___________
1. Solve the system by graphing:
a.
x + y = -2
b.
y = 4x + 4
-2x +3y = 6
y = -x + 2
2. A wilderness group is selling cans of nuts and boxes of microwaveable popcorn to raise money for a
trip. A can of nuts sells for $4.50 and a box of microwaveable popcorn sells for $3. The group
sells $252 in nuts and popcorn and they sell twice as many boxes of popcorn as cans of nuts.
a. Let x be the number of boxes of popcorn and let y be the number of cans of nuts sold.
Write an equation that relates the number of boxes of popcorn sold to the number of cans
of nuts sold.
b. How many boxes of popcorn did the group sell? How many cans of nuts did the group sell?
3. Solve the system by substitution.
a. y = x + 8
y = 9x
b. 3x + 2y = -4
y = 4x - 2
4. Solve by addition.
a. 3x + 6y = 9
x – 6y = 11
b. -3x+ 4y = -5
5x + 4y = -13
5. Solve the system by elimination.
a. 3x – 4y = 21
4x + 2y = 6
b. 2x – 6y = -18
3x + 7y = 37
6. For a school fund raiser, Jay sold 12 boxes of stationery and 8 boxes of envelopes, for a total
of $41.00 Sue sold 18 boxes of stationery and 16 boxes of envelopes, for a total of $68.50.
How much did one box of envelopes cost?
7. Find two numbers whose sum is 33 and whose difference 13.
8. At a garden shop, a customer pays $48 for 5 geraniums and 4 lilies. Another customer pays $58
for 4 geraniums and 6 lilies. Find the cost of one geranium and one lily.
9. Describe the solution(s) of the system.
6x + 4y = 10
18x + 12 y = -20
a. no solution
b. (-7, 13)
c. (7, -8)
d. (-1, 4)
10. Which choice best describes the solution(s) of the system of equations?
-24x + 8y = 24
a. (1, 48)
b. (-1, 0)
-15x + 5y = 15
c. Infinitely many
d. no solution
11. Express each equation in slope-intercept form. Then determine, without solving the system,
whether the system of equations has exactly one solution, no solution, or an infinite number of
solutions.
15x + 5y = 5
-6x – 2y = -2
12. Explain why the system of equations below has no solution.
13. Solve the system of inequalities graphically:
a. y < 3x + 1
y>x-3
b.
-3x + 3y < 6
12x + 6y > 18
y = -5x + 2
5x + y = -1
14. Write a system of linear inequalities that defines the shaded region.
y
10
–10
10
–10
x