Topic 4 Test

Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

x − 2y = 3

y = −2x + 6

• infinitely many solutions

• One Solution: (0,3)

• one solution: (3, 0)

• no solution

Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

x + y = 3

3x − 2y = 4

• infinitely many solutions

• one solution: (2, 1)

• one solution: (1, 2)

• no solution

Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

2x = −4y + 10

6y = −3x + 12

• infinitely many solutions

• one solution: (12, 15)

• one solution: (15, 12)

• no solution

Write a system of linear equations that has infinitely many solutions.

• x − 2y = 3; 3y = −6x + 18

• 2x + 2y = 6; 3x − 2y = 4

• 2x = −4y + 10; 6y = −3x + 12

• y = 2x − 5; −4x + 2y = −10

Solve the system using substitution.

x + 2y = −1

2x − 3y = 12

• (3, −2)

• (−3, 2)

• (−2, 3)

• (2, −3)

Solve the system using substitution.

7x = 2y + 1

4y = −3x + 15

• (−1, 3)

• (1, 3)

• (1, −3)

• (−1, −3)

Solve the system using substitution.

x+y/2=4

x/3+2y=5

• (3, 2)

• (−3, 2)

• (3, −2)

• (−3, −2)

A change purse contains a total of 100 nickels and dimes. The total value of the coins is $7. How many coins of each type does the purse contain?

• 60 dimes and 50 nickels

• 50 dimes and 50 nickels

• 40 dimes and 60 nickels

• 35 dimes and 65 nickels

Solve the system of inequalities by graphing.

2x + 3y ≤ 6

3x + 2y ≤ 6

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Solve the system of inequalities by graphing.

x + y ≥ 9

3x + y ≥ 12

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