Systems of Equations

Solving

100

2(3x-5)=6x–4

What is no solution?

200

x+x/3=4

What is x=3?

300

(x-3)(x+4)=x²+4

What is x=16?

400

|2x–3|=5

What is x=4 and x=-1?

500

Solve for y:

2x²+2y=4x+2x²–7

What is y=2x–7/2?

Solving Systems by Graphing

100

The number of solutions for the system:

y = 2x + 7
y = 2x + 5

What is none?

200

The solution to the system of equations:

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

What is (0, -2)?

300

The solution to the system of equations:

y = -3
x = 5

What is (5, -3)

400

The solution to the system of equations

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

What is (3, -2)

500

The solution to the system of equations:

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

What is no solution?

Solving Systems by Elimination

100

The solution to the system of equations:

x + y = -6
x - y = -10

What is (-8, 2)?

200

The solution to the system:

8x + 5y = 9
2x - 5y = -4

What is (0.5, 1)?

300

The solution to the system:

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

What is (-15, 12)?

400

The solution to the system

2x - 4y = 12
-8x + 16y = -48

What is infinitely many solutions?

500

The solution to the system:

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

What is (24, 8)

Solving Systems by Substitution

100

The solution to the system:

x = 4y
2x + 3y = 22

What is (8, 2)

200

The solution to the system

y = x - 2
3x - y = 16

What is (7, 5)

300

The solution to the system

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

What is (3, 8)

400

The solution to the system

3x - 2y = 4
y = 2x - 1

What is (-2, -5)?

500

The solution to the system

x + y = 12
x = (1/3)y

What is (3, 9)?

Systems Word Problems

100

The sum of two numbers is 104. Their difference is 68. What is one of the numbers?

What are 86 and 18?

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

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

The dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width

What is 26x13?

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?