Systems of Equations

Solving by Graphing

100

Solve the system by graphing:

y = x + 4
y = 2x + 5

(-1, 3)

200

Solve the system by graphing:

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

(0, -2)

300

Solve the system by graphing:

y = -3x + 8
y = x+ 1

(2, 2)

400

Solve the system by graphing:

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

(3, -2)

500

Solve the system by graphing:

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

No solution

Solving by Elimination

100

Solve the system by addition/elimination:

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

(-8, 2)

200

Solve the system by addition/elimination:

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

(0.5, 1)

300

Solve the system by addition/elimination:

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

(-15, 12)

400

Solve the system by addition/elimination:

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

Infinitely many solutions

500

The solution to the system:

4x + 3y = 120
8x - 12y = 96

(24, 8)

Solving by Substitution

100

Solve the system by substitution:

x = 4y
2x + 3y = 22

(8, 2)

200

Solve the system by substitution:

y = x - 2
3x - y = 16

(7, 5)

300

Solve the system by substitution:

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

(3, 8)

400

Solve the system by substitution:

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

(-2, -5)

500

Solve the system by substitution:

x + y = 12
3y - x = 0

(3, 9)

Word Problems

100

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