Solving Systems
Word Problems and Systems
Multiplying Polynomials
Solving Equations
Chapters 1-3
100
Solve the system:
y = 7x - 5
2x + y = 13
(2 , 9)
100
The math club and the science club had fundraisers to buy supplies for a children’s hospital. The math club spent $135 buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled water cost? Write and solve a system.
$20 / case of juice
$15 / case of water
100
Complete the generic rectangle and write the area as a product and as a sum.
Product: (2x - 8)(5x + 9)
Sum: 10x2 - 22x - 72
100
Solve:
5x - 4(x - 3) = 8
x = -4
100
Solve for y:
5x + 3y = 15
y=-5/3x+5
200
Solve the system:
y = 2x - 3
-2x + y = 1
No Solution
200
Suppose that you have $75 in your savings account and you save an additional $5 per week. Your friend has $30 in his savings account and saves an additional $10 per week. In how many weeks will you both have the same amount of money in your account? How much money will be in your accounts? Write and solve a system of equations.
9 weeks
$120
200
Find the product:
(6x - 2)(6x + 2)
36x2 - 4
200
Solve:
|2x + 3| = -7
No Solution
200
Name the domain and range:
Domain: x ≤ 4
Range: All Real Numbers
300
Solve the system:
4x + 2y = 6
y = 3 - 2x
Infinitely Many Solutions
300
On a special day, tickets for a minor league baseball game cost $5 for adults and $1 for students. The attendance that day was 1,139 and $3,067 was collected. Write and solve a system of equations to find the number of adults and the number of students that attended the game.
482 adults
657 students
300
Find the product.
(x2 + 2x - 9)(x + 7)
x3 + 9x2 + 5x - 63
300
Solve:
4y - 2(6 - y) = 6
y = 3
300
Find the equation of the line that goes through the points (-12 , 14) and (9 , 0).
y=-2/3x+6
400
Solve the system:
2x-y=4
1/2x+y=1
(2 , 0)
400
A quilt maker sews both large and small quilts. A large quilt requires 8 yards of fabric while the small quilt requires 3 yards. How many of each size quilt did she make if she used a total of 90 yards of fabric to make 15 quilts? Write and solve a system of equations.
6 small quilts
9 large quilts
400
Find the product.
(3x + 4)2
9x2 + 24x + 16
400
Solve:|3 - 2x| = 7
x = -2 or x = 5
400
Write an equation represents the number of tiles in each figure of the pattern. (x represents the figure number and y represents the number of tiles.)
y = 3x + 7
500
Solve the system:
8x - 7y = 5
3x - 5y = 9
(-2 , -3)
500
Your science test is worth 100 points and contains 38 questions. There are two-point and five-point questions on the test. How many of each type of question are on the test? Write and solve a system of equations.
30 two-point questions
8 five-point questions
500
Find the product.
(2x2 - 5)2
4x4 - 20x2 + 25
500
Solve:
(x - 3)(x + 5) = x2 - 7x - 15
x = 0
500
Simplify using only positive exponents:
(-3x-2y3z)4
(81y^12z^4)/x^8