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3 Variables
Solving by Graphing
Solving by Elimination
Solving by Substitution
Word Problems
100

Determine the number of solutions of the linear system:

x – 5z = 7

x – 5y + 3z = 8

7z = 14


What is (17, 3, 2)

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

Two lines have the following equations: 

x+3y-z = 7

x+2z = -2

4z = 8

At what point do they intersect?

What is (-6, 5, 2)?

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

What is the solution for the system of equations below?

x + y + z = 2

x - 2y - z = -4

x - 9y + z = -18

A) (-2, 2, 2)

B) (0, 2, 0)

C) (-2, -2, 6)

D) (0, 2, 4)

What is B? (0, 2, 0)

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

A food store makes a 11-lb mixture of peanuts (x), cashews (y), and raisins (z). Peanuts cost $2.00 per pound, cashews cost $3.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $23.00. Write but do not solve.

What is...

2x + 3y +1z = 23

x = 2y

x + y + z = 11

?

400

Graph and Solve:

y > 2.5x+4
y < 2.5x

What is no solution?

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

4x+y= -10z

4x+y = -7z

4x+y = 8z

These three planes intersect at a line. The infinite solutions that are on this line "4x+y=0". 

500

Is (0, 3) a solution to this systems of inequalities?

y - 3x < 3
2y < 6x +6

No. 

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?