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Miscellaneous
Solving by Graphing
Solving by Elimination
Solving by Substitution
Word Problems
100

Without graphing, explain why this system of equations would result in a special case. Please be detailed in your explanation: 

y = -3x + 2

y = -3x - 5

These lines are parallel since they have the same slope and different y-intercepts. If the lines do not intersect, which is the case with parallel lines, there will be no solution.

100
The quadrant in which the solution to the following system lies:

y = x + 4
y = 2x + 5

What is II
100
The solution to the system of equations:

r + s = -6
r - s = -10

What is (-8, 2)?
100
The solution to the system:

x = 4y
2x + 3y = 22

What is (8, 2)
100
The sum of two numbers is 104. Their difference is 68. What are the numbers?
What are 86 and 18?
200

Solve this system via substitution: 

-x - 7y = -20

-8x - 4y = -20

x = 1

y = 3

200
The solution to the system of equations:

y = 3x - 2
y = -x - 2

What is (0, -2)?
200
The solution to the system:

8a + 5b = 9
2a - 5b = -4

What is (0.5, 1)?
200
The solution to the system

y = x - 2
3x - y = 16

What is (7, 5)
200
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
What is $30?
300

Solve this system by elimination: 

-3x + 5y = -11

5x - 3y = 29

x = 7 

y = 2

300
The solution to the system of equations:

y = -3
x = 5

What is (5, -3)
300
The solution to the system:

2x + 3y = 6
3x + 5y = 15

What is (-15, 12)?
300
The solution to the system

y = 3x - 1
7x + 2y = 37

What is (3, 8)
300
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
What is 400 advanced tickets, 200 game-day tickets?
400

Solve this system using elimination or substitution: 

1/2 x + 5/4 y = -6

4/3 x - 1/2 y = -2/3 

x = -2

y = -4

400
The solution to the system of equations

y = (1/3)x - 3
2x - y = 8

What is (3, -2)
400
The solution to the system

2a - 4b = 12
-8a + 16b = -48

What is infinitely many solutions?
400
The solution to the system

3s - 2t = 4
t = 2s - 1

What is (-2, -5)
400
The dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width
What is 26x13?
500

Two bananas and three apples cost $2.90. Three bananas and two apples cost $3.10. Find the cost of one banana and one apple. Define your variables, write a system of equations, solve, and write your answer as a sentence.

A banana cost 70 cents and an apple costs 50 cents.

500
The solution to the system of equations:

y - 3x = 3
y = 3x - 2

What is no solution?
500
The solution to the system:

(1/3)x + (1/4)y = 10
(1/3)x - (1/2)y = 4

What is (24, 8)
500
The solution to the system

t + u = 12
t = (1/3)u

What is (3, 9)?
500

The amount of money each child received when Mr. Vogel left $25,000 divided between his son and daughter, with the daughter receiving $5000 less than the son.

What is $15,000 for the son and $10,000 for the daughter?